When 'READY' appears on the screen the time starts, and then it stops at the last pellet collected as normal.

The difficulties are there for people who have a run that got a better time on a level than they would have, and also the AI differences(like on Hard). Maze is there for those who don't want to do a run for the IL. Also, in Maze you would be able to die and get a quicker time on certain levels without it affecting your run.

ILs for the difficulties would just have to be timed out of a run, yes. Which is also why Maze is a separate category.