CORS today is just an annoying artifact of a poorly conceived idea about domain names somehow being a meaningful security boundary. It never amounted to anything more than a server asking the client not to do something with no mechanism to force the client to comply and no direct way for the server to tell if the client is complying. It has never offered any security value, workarounds were developed before it even became a settled standard. It's so much more likely to prevent legitimate use than protect against illegitimate use that browsers typically include a way to turn it off.
With CSRF the idea is that the server wants to be able verify that a request from a client is one it invited (most commonly that a POST comes from a form that it served in an earlier GET). It's entirely up to the server to design the mechanism for that, the client typically has no idea its happening (it's just feeding back to the server on a later request something it got from the server on a previous request). Also notable is despite the "cross-site" part of the name it doesn't really have any direct relationship to "sites" or domains, servers can and do use the exact same mechanisms to detect or prevent issues like accidentally submitting the same form twice.