on time = punctual, not late
If something happens on time, it happens at the time that was planned:

• The 11.45 train left on time. (= it left at 11.45)
• Please be on time. Don’t be late.
• The conference was well-organised. Everything began and finished on time.

in time (for something / to do something) = soon enough

• Will you be home in time for dinner? (= soon enough for dinner)
• I sent Amy a birthday present. I hope it arrives in time. (= on or before her birthday)
• I’m in a hurry. I want to get home in time to watch the game on TV. (= soon enough to see the game)

The opposite of in time is too late:

• I got home too late to watch the game on TV.

You can say just in time (= almost too late):

• We got to the station just in time for our train.
• A child ran into the road in front of the car, but I managed to stop just in time.