There are some examples that there are similar problems in math contests (I can't distinguish if it's deliberately copied from math contests or just a coincidence).

317E Princess and Her Shadow, which is almost the same as a problem from Canadian National Olympiad link

618F Double Knapsack, see the discussion here

1684H Hard Cut, see the discussion here

K in Yuhao Du Contest 5. Yes, I admit the idea is from a problem in All-Russian MO link

Sometimes authors just learn the idea from MO problems. But sometimes, the problem is just identical (like 1684H).

I don't think there is much difference between copying problems from math contests and copying problems from an old opencup contest. However, the community seems much more tolerable of copying problems from math contests.

Maybe the difference is that the opencup problems are known to more participants. So copying problems from math contests has less impact.