Are cookies automatically set and sent on future requests?

[cannikin]

I'm making some API requests that set and require cookies in order to respond (weird, I know, but it's a third party API). I'm noticing that if I do not capture the cookie and present it in the next request, it still works as if I did! Is posting actually storing and sending cookies automatically? I don't see anything listed in Headers so I wouldn't have thought so, but I don't know how else this API is responding to the correct user...