What does it take to 51% a PoS chain?

Hey, we're all familiar with "control 51% of the hashing power of a PoW chain = double spending/etc attack". But what about PoS?

As I understand it, you still need to control 51% of the validators, but you have to stake each one at (currently, 32) some fixed ETH amount. But this doesn't mean that you need to control 51% of ETH, right? Just enough ETH for staking so that you can run 51% of the nodes?

Obviously this is much, much riskier than the PoW attack from an attacker's standpoint, but I want to clearly understand the technicals here.

Additionally, some of the reading I've done suggests that the mitigation procedures for after a 51% attack takes place are different for PoW vs PoS chains, and I'd love to understand better.