There are three types of statisticians;

 1. those that (prefer to) work with real data,
 2. those that (prefer to) work with simulated data,
 3. those that (prefer to) work with the symbol $X$.

math stat types would be (3). Typically, type 
(1) statisticians have some prefix attached to 
make clear the *source* of the data they work with 
(biostatistics, econometrics, psychometrics,....) 
because these fields have implicit shared 
assumptions about the data they use and the ordering
of the plausibility of these assumptions.