Mix = Mixes all selected (audio or VI) tracks for the time selection to a single stereo audio file.
Render = Renders each selected (audio or VI) track for the time selection to its own stereo audio file.
Please put these definitions in the help for the "mix or render audio" screen. I was going to write to ask about this and was glad to find it in the forums, but I found it a full two months after I first had a question about it, and I had searched the help extensively for the answer at that time without finding it.