Yeah, you have both of those correct. You time a full game run using the actual real world time passed, you time individual levels by what the scoreboard says at the end (even in cases where it is not accurate, such as for PAL)

The in game timer doesn't appear to be any different. i.e. it seems to be tied to frames, rather than real world time. JP/US versions are definitely faster for full game runs however, since they are RTA instead of IGT.