What is the difference between normal and IID? What is the difference between a normal distribution and an independent and identical distribution? 
 A: These terms come up in various applications in statistics.  Perhaps the most common situation would be a simple linear (OLS) regression.  In that case, we say that the residuals (really the errors) should meet the following assumptions:  


*

*They are independent

*They have constant variance

*They are normally distributed


If they are independent and identically distributed (IID), then they must meet the first two criteria (since differing variances constitute non-identical distributions).  However, IID data need not be normally distributed.  For instance, imagine a set of data where each datum is independently drawn from the same uniform distribution.  Then they would be independent, and they would have the same distribution, but that distribution would not be normal.  
On the other hand, a set of data can be normally distributed, but with subsets that follow different normal distributions (e.g., different means or different variances).  In addition, you could have two subsets that are dependent:  For example, the second subset could be generated by adding $1$ to every value in the first subset.  In that case, the subsets would be dependent in that, if you knew the relevant first value, you could deduce the second value.  Nonetheless, both subsets would be normally distributed.  
Thus, whether or not a set of data is IID is unrelated to whether they are normal.  
