Differencebetween.net says: “The common terms being used today are “log in” and “sign up” which are interchangeable with “sign in” and “signup”. You can see both sign up and signup are synonymous and different websites use them differently. Similarly, sign in and log in are synonymous with each other and are used basically for the same purpose – that is to authenticate yourself to an account that is already created by you. Sign up simply refers to the process of registering yourself to create an account. They both are all over the internet and the difference is quite subtle.” Here is the link to the full explanation including the terms: “sign up” and “register”: http://www.differencebetween.net/technology/difference-between-login-and-sign-up/

“Sign in” is also used in non-computer related situations. If you attend a course, they may ask you to sign in on a list of students. “Login” would never be used in this situation.