The theoretical statistician uses x, the applied statistician uses y (because we reserve x for predictors).

The goal of the applied statistician is to answer "y?"

An applied statistician knows worth of "y".

A theoretical statistician knows all about measure theory but has never seen a measurement whereas the actual use of measure theory by the applied statistician is a set of measure zero.

The goal of the applied statistician is to answer "y?"

An applied statistician knows worth of "y".

A theoretical statistician knows all about measure theory but has never seen a measurement whereas the actual use of measure theory by the applied statistician is a set of measure zero.