"Log in" and "log out" are verbs. "Use this form to log in. Click this icon to log out."
"Login" and "logout" are adjectives. "Visit the login screen. The logout process is complete."
They can also be nouns. "Login was successful. So was logout."
I'm just posting this because I'm tired of seeing things like "Click here to login" everywhere.
"Sign up" is the same way — you can sign up for a meeting on the signup page.