If track logging isn't turned off (setup/tracks/tracklog set to one of the 'record' options), your every movement is logged in the current track, irrespective of any navigation you may or may not be doing.
So, with track logging enabled, navigate a track (or route, or 'go to' a POI or waypoint, or just wander about without using the navigation functions), and "Current Track" will contain a log of your movements since it was last reset.
Ah. I think I see where the confusion comes from: "Current Track" in the tracks list means "the track I am currently recording" *not* "the track I am currently navigating"
When you've finished your ride, you can save the contents of "Current Track" by clicking on it and selecting save.