Yeah, those two phrases look too similar. What happened to good old "login" anyway?

from the meeting where it was explained to me that we couldn't use "login", it is too technical-sounding and not friendly enough. "log in" is computer language, "sign in" is human language.

What is the origin of sign in? I imagine the old days when you needed to sign a book when entering premises? Is this the floppy disk for save action of web jargon?

That's exactly it - you sign the guestbook when you arrive at the hotel.

You want to enter a site you're already on?

As I said, English is not my native tongue. Choose whatever synonyms are appropriate. Even google translate gets confused. If I enter "sing in" it translates it to Spanish as "registrarse" which is actually "sign up"! How about using enroll, or register instead of "sign up"?