What is the difference between statistics and biostatistics? It occurred to me that, while I've pieced together some ideas over the years about the differences between statistics and biostatistics, I've never heard a formal explanation.  What is the distinction between these two disciplines (currently)?  And why did this distinction begin in the first place?
EDIT: I've not been specific enough in my original question.  I understand that biostatistics is the application and development of statistics in the biomedical field.  But what are some specific examples of the distinctions?  For example, what distinguishes graduate education in the two fields?  What is the purpose of having distinct academic departments for the two disciplines (a distinction I see in no other field)?
 A: To quote the "Encyclopedic dictionary of mathematics" by Kiyosi Itô (ed.):
In many applied fields there exist systems of statistical methods which have been developed specifically for the respective fields, and although all of them are based essentially on the same general principles of statistical inference, each has its own special techniques and procedures. Specific names have been invented, such as biometrics, econometrics, psychometrics, technometrics, sociometrics, etc.
A: As someone who took courses from the Statistics department of a university which did not offer a Biostatistics major and worked in clinical trials with biostatisticians and read many papers written by biostatisticians, I can offer a particular perspective.  I see biostatistics as a field that applies a subset of standard statistical techniques to clinical research.  Biostatistics focuses on categorical variables and logistic regression to a greater degree than statistics applied to subjects studied in the physical sciences and engineering.  Biostatistics tends to seek answers to binary questions, such as these: 1) Is this subject healthy or sick? or 2) does this drug cause more good than harm?  It often uses discrete independent variables such as whether a subject was alive or dead at the end of the study.  This isn't an ironclad distinction, though: biostatistics also uses survival analysis, which involves measuring a continuous variable, i.e., the length of time to an event of biological significance.
A: I will take a swing at answering this from the perspective of someone who is neither a statistician nor a biostatistician. Rather, I exist in the blurry grey area that is "epidemiological methods".
As other posters have mentioned, biostatistics is a discipline particularly focused on statistics as they apply to biological problems - including those that arise in medicine. While this seems somewhat semantic, it does result in some things that I think it make it a distinct entity on its own, though none of these are strictly exclusive:


*

*A reliance on subject-matter expertise. Be this through collaboration with subject matter experts, or simply working on the same problem for a long time, biostats involves the fusion of a statistical method with a particularly applied problem.

*A common and fairly restricted set of study designs. While exotic study designs are growing more acceptable, by and large the field is still dominated by cohort, case-control and clinical trial designs. The focus is often on estimating categorical exposures (given the drug, not given the drug...) and categorical outcomes (died, didn't die).

*A ubiquity of missing/misclassified/poor data.

*Less emphasis on classification and prediction. As @Alexis has mentioned, causal inference, and the desire to explore counterfactuals is hugely important for biostatistics. While not exclusively true, something that is a good predictor but has no etiologic explanation is of less interest. This has, for example, somewhat limited the penetration of machine learning methods.

A: Biostatistics, biometrics and biometry are synonyms. Medical statistics (sometimes called 'clinical biostatistics' for no clear reason) is a subset of these.
A: Statistics vs. Biostatistics does not make sense as a comparison; biostatistics is really a sub topic of statistics. This would be like asking "what's the difference between mathematics and probability?"; probability is a subfield of mathematics. 
As others have noted, biostatistics applies to problems that are very common in both medical studies and biological research. This includes, but certainly is not limited to, survival analysis, sequential trial design, longitudinal analysis and genomic analyses, to name only a few topics. 
As for the difference between programs in statistics and biostatistics, the obvious difference between two programs is that the biostatistics programs will be specializing in the topics above. Most statistics programs will still cover biostatistics (for example, I have my PhD in Statistics, and of all possible specializations of statistician, I am most qualified as a biostatistician, my current position), but it is definitely possible to get a PhD in statistics with only a mild introduction to biostatistic-specific topics. 
It's my understanding that the high demand for statisticians by pharmaceutical companies lead to the demand for biostatistics programs. 
A: I see the answers here just define the domain of work so I try to give a more comprehensive answer based on my experience of learning statistics as a medical practitioner. Most of my experience is on clinical trials, but this can be applied to any domain of biostatistics.
The purpose of biostatistics is biological and medical field, this gives it subtle differences according to this purpose.
Statistics is all the same! it is just math! However, here is the difference that comes to my head when I define biostatistics.
1- Ordinary statistician will not understand all the terminologies in biostatistics but he will understand the math!
Both of them are coming from mathematical and probability theories. So you will find most of the tests resonates will with both words like regression analysis, t-test ... etc
However, when it comes some other tests like relative risk, attributable risk reduction, kaplen mieir curves ... etc these few tests will sound strange for someone with no biostatistical knowledge. However, they can easily go through it when they read about these tests
2- Biostatistics field usually don't reinvent the wheel, they just enhance what is available
As I said biostatistics is built on statistics. But unlike the previous point, most of the current active research on biostatistics is mostly about enhancing few properties of existing test with different terminology to serve the purpose of biostatistics. For example, something like overall survival or time-to-death are all terminologies exclusive for biostatistics (that's for sure or who would study life and death) however they are built on time-to-event analysis that biostatistician has created these terminologies to make the test serve the purpose of biostatistics, more standardized and easy to interpret in among medical practitioners. 
3- Biostatistics has its specific guidelines (just like any other field) however it is more strict.
Biostatistics has established many guidelines and conventions to analyze the data of different field. For example, statisticians working in biology and genomics are doing different tests and have different thinking than who are working in clinical trials(and of course who are working in business intelligence). But this way of working is considered fixed among the community of biostatistician, so a biostatistician don't usually think out of the box unless there is something urges that has not existed before, and this usually don't happen as study design of biostatistics fields is very definitive. 
A clearer example of this is the baysian statistics application on biostatistics. Bayesian statistics are known to be flexible, so you will not find a lot of usage of this type of statistics. Also, this usage is tied to a certain repetitive application like sensitivity measurement. There is no need to think of probabilities when there are easier options that are easier to interpret and perform.
Why This restriction?
1. The community is trying to avoid p hacking and beautifying the results. Especially if you are working in clinical trials, you don't just use the tests the gives the best results. You even don't use one-sided tests usually! These conventions are there to protect the trials validity and anything else will make the community suspicious.


*That's the most important part. All the work of biostatistics should be interpreted by a medical practitioner, so he should make some sense of results himself. So they try to stick to a few approaches.

*This point is unfair because there is no comparison, but study design in biostatistics is very definitive. Usually, you don't have to think a lot on how to prove the efficacy of a drug or adverse effect or so. So it is very unlikely you will need to keep your head busy of learning different techniques and tests every while as it is very rare to see a pattern change. 
That's all I have right now, I will update my answer if I remembered something else. 
A: When I look at the Wikipedia entry for biostatistics, the relation to biometrics doesn't seem so obvious to me since, historically, biometrics was more concerned with characterizing individuals by some phenotypes of interest, with large applications in population genetics (as exemplified by the work of Fisher), whereas part of this discipline now focus on biometric systems (whose objectives are the "recognition or identification of individuals based on some physical or behavioral characteristics that are intrinsically unique for each individual", according to Boulgouris et al., Biometrics, 2010). Anyway, there still are reviews like Biometrika and Biometrics; although I read the latter on an irregular basis, most articles focus on "biostatistical" theoretical or applied work. The same applies for Biostatistics. By "biostatistical" applications, I mean that it has to do with applications or models related to the biomedical domain, in a wide sense (biology, health science, genetics, etc.). 
According to the Encyclopedia of Biostatistics (2005, 2nd ed.), 

(...) As is clear from the above examples,
  biostatistics is problem oriented. It
  is specifically directed to questions
  that arise in biomedical science. The
  methods of biostatistics are the
  methods of statistics -- concepts
  directed at variation in observations
  and methods for extracting information
  from observations in the face of
  variation from various sources, but
  notably from variation in the
  responses of living organisms and
  particularly human beings under study.
  Biostatistical activity spans a broad
  range of scientific inquiry, from the
  basic structure and functions of human
  beings, through the interactions of
  human beings with their environment,
  including problems of environmental
  toxicities and sanitation, health
  enhancement and education, disease
  prevention and therapy, the
  organization of health care systems
  and health care financing.

In sum, I think that Biostatistics is part of a super-family--Statistics--, and share most of its methods, but has a more focused area of interest (hence, an historical background, specific designs, and a general theoretical framework) and dedicated modeling strategies.
A: As for what I see this seems to be just a matter of semantics. Statistics applied to research or testing in the social sciences is just called Statistics. A person working with this type of situations needs to have a through knowledge of his or her field before applying a statistical procedure. Anyway we just call it Statistics. I think that this discussion is just about a system of preferences. If in  the biological fields it is preferred to call it biostatistics there is no problem. This is just a choice of words.
A: There is not a significant difference between statistics and biostatistics. In my definition, biostatistics is the application of statistics to biology. So a Biostatistician has a relatively strong command in biology, well at least enough to understand how to apply his statistics to biology. 
It would be the same concept as Artstatistics, or Sociostatistics; application of statistics to art or statistics to sociology, respectively.
 Biostatistics is simply the statistics of BIOLOGY. So you need a command of biology and statistics to do well as a Biostatistician.'Tis all.
