Shoutbox

It's possible that when you open your Hotmail inbox that you get signed in there too.  When you're signed in, if you click to sign out it should give you the options to sign out from locations.  If they're both the same then it means its the same computer.  You can disable auto-sign in whilst signed into Hotmail, it gives you an option in the top right, just next to "Options" it will show your Messenger status, if you click there you can tell it not to sign you in automatically when you open hotmail