The session is a complete cycle of the user logging in and then after the work is done, logging out. The 'Log' includes the number of sessions per user. I'm acquainted with webmastership as well and it's interesting to know that during our audit, we check the log. Note that all these portals uses sign up for the process of first time registration and not log up. Facebook, ELL and COCA calls it Log in, whereas Google, Twitter, Bank of America and LinkedIn uses Sign in. Well, both mean same that you enter somewhere where you are already registered. What is interesting is sign in and log in. For instance, if you are new to Twitter, you need to sign up first. So when you visit and access anything for the first time, you need to sign up.

It could be portal, newsletter or things the like. You mentioned log-in and that's what makes me think that you probably want to know the difference in the context of Internet. While Hellion describes those terms in general, I am writing here in the context of the cyberworld that also includes the gadgets.

What is another word for sign up sheet