exit tmux window without quitting the Terminal program

Detach from currently attached session

Session

Ctrl+ b d or Ctrl+ b :detach

Screen

Ctrl+ a Ctrl+ d or Ctrl+ a :detach

The previous answers are incomplete, I believe. What :detach does is to shut down the viewports that are displaying tmux activity. However, tmux itself is still running in the background as you can see by running ps:

myuser 1799 0.0 0.0 2500052 4632 ?? Ss 21Feb16 0:48.39 tmux new-session -s Dev

In fact, even if you quit terminal and start it up again, any tmux processes are STILL running in the background.

To actually kill the tmux process itself, you have to do:

tmux kill-session [-t session_name]

or simply:

kill -9 1799