When using a Remote Desktop Connection with a solution like Terminal Server, Thinstuff or Windows RDP, there is a significant different between logging out and disconnecting.
If you simply click the X on the remote connection bar at the top of the screen, you are only disconnecting. Think of this as turning off your monitor. In other words, your session remains active and all programs you were accessing remain open. While this might be convenient because you don’t have to reopen everything when you reconnect, there are drawbacks. For example, if you are accessing a program that has limited user or only one user, you are tying up that user so that no one else can access the program. Some programs like Tabs and PracticeMaster might require everyone out of the program for maintenance purposes. By simply disconnecting, you are still logged in and are preventing that maintenance.
If you click the start button and select Log Off, you are logging out of all programs and closing the session entirely. Think of this as a restart. This frees up any connections, resets programs, etc.
Typically, you want to Log Off. Logging Off means you are releasing any licenses you are using so that the next person can use them. It also makes sure your session is closed for maintenance, backup or other things that an open session might interfere with.