The difference between both session_unset and session_destroy is as follows:
session_unset just clears out the sesison for usage. The session is still on the users computer. Note that by using session_unset, the variable still exists.
Using session_unset in tandem with session_destroy however, is a much more effective means of actually clearing out data. As stated in the example above, this works very well, cross browser:
I noticed that in firefox, one could simply use sesison_unset and the session would be cleared. When trying this on IE, I was horrified to find out that the data was still there, so I had to use session destroy.