I don't think there is any difference. If your network disconnects you will eventually leave the meeting as well. If you have a recording going on it will continue to record until everyone has left the meeting (or 4 hour limit has been reached).
There is no "End meeting" as such. Meeting actually continues in a chat and people can rejoin it later again.
I am sorry to hear the details. The conference ends and when you disconnect from the handset picture, the conference remains on the display with the most recently used items. However, if you click “Exit” to disconnect, the meeting ends and does not remain in your most recently used items. What is the difference?