You have stated the difference very clearly but here is a pair of contrasting sentences anyway.
I was expected to arrive at 3 pm. I was neither late nor early I arrived at exactly 3pm.
- I arrived on time for the meeting.
I was expected to arrive at 3 pm. I arrived at 2.55 pm. I was not late.
- I arrived in time for the meeting.
'in time' is often used when you thought you were going to be late for something but arrived on time.
If you want to say that you arrived much earlier than needed, in British English you could add the words 'plenty of'.
- I arrived in plenty of time.