The Explaination of These words （log in, log on, signon, sign on, sign in）

A login (also log in, log on, signon, sign on, sign in) is the process of receiving access to a computer system by identification of the user in order to obtain credentials to permit access. It is an integral part of computer security procedure.

sign-up：
1、Engage by written agreement
2、Joining a club, an activity, etc. With the intention to join or participate, "Sign up for yoga classes."