Difference between 'in time' and 'on time' ?

To reach on time indicates that someone/something reached  at the  scheduled or expected time. He/she is neither early nor late.

Example: The Board meeting started on time ( It was scheduled to start at 3 pm and it did start at that time) * The train was scheduled to arrive at 7 pm and it reached on time. 

To reach in time indicates that someone/something reached before the schedule time.

Example: The film was scheduled to start at 8 pm and we reached in time ( before the show started).

When you are on time, you are not late but you don’t have any spare time. When you are in time, you actually reach before the scheduled time and you have some spare time to relax.