One relevant distinction: those who follow the rules, and those who discover them. Or the theory builders and the problem solvers.

Consider something like set theory. When set theory entered a period of crisis in the early 20th century, there were those who mathematicians, logicians, and philosophers who tried to determine what a good formalization of the notion of set is. Russell and Leśniewski come to mind, for example. Naturally, this isn't just a matter of coming up with any collection of axioms. It involves analyzing the concept of "set".

This is different from the Erdos's of the world.