which is close enough to "login", which is widely understood (I do have the same issue with "sign in" VS "sign up", I know the difference, but as a non-native speaker it also takes me a second, or sometimes one is more prominent than the other and I mistakenly click on it, etc).

But whatever, ("Sign in" or "Log in") alongside "Register" is clear enough. "Sign in" alongside "Sign up" is confusing. Thanks Al-Khwarizmi for bringing that up... or is it bring in ? ;)