In machine learning, what can be called a classifier? Is the word classifier used for algorithms that solely classify things, such as Logistic Regression, SVMs, or Neural Networks, or can it be used for all Machine Learning algorithms? In other words, can Linear Regression be called a Classifier?
If not, what word can be used to refer to any and all machine learning algorithms (I feel like algorithm is too generic).

Update: All the answers state that Linear Regression should not be considered a classifier. According to SeanEaster, a better term would be Regressor. I've decided to go with that. Thanks to everyone who took the time to explain this to me.
 A: From the lovely book Introduction to Statistical Learning:

We tend to refer to problems with a quantitative response as regression problems, while those involving a qualitative response are often referred to as classification problems

So, no Linear Regression should not be called a classifier.
I guess you can't be much more specific than referring to all methods that solve some kind of learning problem as machine learning algorithm or statistical learning method.
A: Bishop writes:

Applications in which the training data comprises examples of the
  input vectors along with their corresponding target vectors are known
  as supervised learning problems. Cases such as the digit recognition
  example, in which the aim is to assign each input vector to one of a
  finite number of discrete categories, are called classification
  problems. If the desired output consists of one or more continuous
  variables, then the task is called regression.

Bishop, C. M. (2006). Pattern recognition and machine learning (1st ed. 20). Springer.
A: Context suggests the broader term "model," prefixed with relevant description. See for example the wikipedia articles for some common learning methods, like artificial neural networks:

In machine learning and cognitive science, artificial neural networks (ANNs) are a family of statistical learning models[...]

Similarly for support vector machines:

In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis.

When being fully precise, I myself would only use "algorithm" in reference to the actual algorithm that trains a model. Using the neural network example, the network itself is a model; back-propagation is an algorithm used to train it. 
In sum, "learning model," "machine learning model," etc. are likely to avoid objection.
As an aside, the term "regressor" is sometimes used as one would use classifier (e.g. this sklearn documentation.) Though this may invite confusion, as the same term can be used for explanatory variables.
A: The major branches of machine learning are supervised learning and unsupervised learning. In supervised learning, there are some target values. In classification problems, you have categorical target values. In regression problems, you have continuous target values.
For example, there are support vector classification (SVM-C) and support vector regression (SVM-R) algorithms.
In unsupervised learning, there are no target values, and no "correct results".
