For purposes of "a place to keep your money", there is very little practical difference. Both types of institution provide checking / savings accounts, both insure your deposited money against bank failure (though through different agencies), both tend to offer loans and other financial services, etc.

The main underlying difference is who "owns" the institution. Those owners want a return on what they put into it. A bank is often part of a publicly traded company, so it's owned by the various people (or institutions) who have bought shares in that company. A smaller bank might be privately owned by a few individuals.

But a credit union is owned by its members: everyone who has an account with them. So the "return" those members get can be through things like lower / no account fees, higher savings interest (though still smaller than you'd get through an online HYSA), lower rates on loans, etc.

Since account holders are owners, you tend to get better treatment at a CU. As a bank customer, you're ultimately a commodity and might get treated as such.

One drawback to a credit union can be (though not always) that as a smaller institution it may have things like the latest online technology for things like bill payment. And a credit union may have particular criteria you have to meet in order to join: live in a given city, go to a given school, member of armed services, etc. Both of those are much less of an issue nowadays, but was a quirk with my own CU 10-15 years ago.

TL/DR: you'd likely get as good (and usually better) services for lower cost at a credit union compared to a bank. Just look for "NCUA insured" (a CU's equivalent of FDIC for banks), though I don't imagine uninsured CUs would be that common.