At the high school and college level, the Olympiads for math and CS are pretty analogous. But there's really popular semi-formal coding contests which exist outside academia which don't really have a math equivalent.
I'd say math contests are more popular among high schoolers, and semi-formal coding contests more popular among college students.
Art of Problem Solving (AoPS) [https://artofproblemsolving.com/] is a really good resource, and there's a very healthy online community.
They're also similar in how olympiads are different from the "real thing" (TM).
As someone who did math olympiads in high school, my 2 cents is that they're a fantastic way to learn how to solve and approach problems and gain intuition. And I'd say intuition mainly comes from solving problems.
