I often have to explain to clients why two “versions” of the same word appear in the text I provide to them. To some, it looks like an error to use “login” and “log in” or “backup” and “back up” in the same document. But it’s not an error. Why the differences? “Login” and “backup” are nouns or adjectives, whereas “log in” and “back up” are verbs (or, if you want to get technical, verb phrases). So:
I use my login to log in.
I back up my computer to my backup drive.
That “log in” and “back up” need to be two separate words when used as verbs becomes immediately clear when you think of them in the past tense.:
I logged in (NOT I logined)
I backed up my hard drive (NOT I backuped)
I logged out (NOT I logouted).
So, if you’re adding a prompt or a button to your website to ask people to log in, it should say “Log In,” not “Login” (and ditto for “Log Out”).
Most of the big sites (PayPal, Google, eBay, Facebook) get this right, but many do not. Have you got it right on your site?