In nontechnical web parlance, log on often means to visit (especially a website), and log in means to sign in with a username and password. For example, we could say you logged on to this website simply by visiting this page, but you won’t be logging in because nothing on this site requires a username and password.
These are not technical terms when used in these senses, and technologically literate people (along with careful writers) might scoff especially at this use of log on. Notwithstanding that, it is common.
Examples
Log on
To learn more about some of these measures, log on to the website. [Houston Chronicle]
Log on to Samsung’s site and it’s blaring out “it’s time for a better tablet”. [Independent]
Then make sure you log on to theage.com.au tonight at 7pm for Real Footy Live, our new AFL finals show. [The Age]
Log in
The password came, but I was still unable to log in. [Guardian]
On your iPhone, you toggle on PhotoStream and log in with your Apple ID. [Wired]
Many Facebook users logged in this morning and found a strange, new social-networking world. [USA Today]