@inthehands You're right of course about one being a noun and the other a verb. Login = the act of logging in (or the credentials you use to do so). I disagree about the labeling, though.
A button saying "log in" is saying "I am the button that allows you to log in." One saying "login" is saying "I am the button that allows you to perform the act of logging in."
"Checkout" and "check out" are a similar noun/verb pair, but there's no confusion about a supermarket sign saying "Checkout."