Facebook Messenger for Windows works only on computers running on Windows 7 Operating System. Once you have Messenger set up on your computer, you can log in and log out by right-clicking the Facebook icon in the your Windows system tray.
Choosing Exit will close the app but still keep you logged into Facebook. Use this option if you want to stop getting notifications but stay logged into Facebook in your browser. After you exit, you can open Messenger again by searching for “Facebook Messenger” in your Windows Start Menu. The app will also open when you restart your computer.
Choosing Log out will completely log you out of both the Messenger app and www.facebook.com. Since Messenger automatically syncs with Facebook in your web browser, we direct you to www.facebook.com to log out. [source]