"In time" means "at the exact time for something."
"On time" means "punctual, not late."
Observe the examples:
I arrived just in time for the presentation.
(I arrived at the exact time the presentation was starting, so I didn't miss anything)
The presenter was scheduled to start at 7pm. And he was on time, but his assistant was not.
(The presenter was not late, he was punctual.)