I have just uploaded my application to my server for the first time and sent the link to a friend, however, when I broused to the site, the site had identified me instead of my friend.

My thinking of what is suppose to happen is that, when I brouse to the site, session variables unique to me are created and are used to track my movement and when someone else goes the the site, a new set of session variables would be created for the second person.

Am I correct with my understanding?

Correct!

Session variables are actually temporary cookies between the BROWSER and the server.

So if YOU opened the site with a different browser on the same machine YOU would have two sessions open.