OK, let me clarify a bit.
ProTrack is array of static cue players. They work no mater of visible state. Menu does not enable them, it just show of hide panel with ProTrack UI.
Click modes - yes, they required for Grid. Mouse event need to be translated somehow into commands, and buttons on toolbar define what to do. Button "ProTrack" has corrreponding command "ClickTrack". I recommend to enable option "Show internal commands" in Configuration dialog, Laser Preview tab. Aniway, i think you are looking for ClickLive command.
Groups - absolutely different "entity". This is more like conception rather than exact functions. ProTrack means you need to keep in mind multiple things - track selection, where track will go, content cues, effects. Not that bad, but still not true obvious. "Group" mode appeared as an answer on question - how to minimize number of places, and make all visually connected? "Group" mode allow to keep effects, destination selection, content and multi-tracking in one single place - grid. This is sort of all-in-one conception.
Hope it helps.
Alexey