I think what you may be asking is, what is the difference between:
He arrived in time for the train.
He arrived on time for the train.
In the first scenario, the message is that:
He arrived within the time allowed to catch the train.
If the train was leaving at 10:13, and the person arrived at 10:12, he arrived within the time required to catch the train.
The second example means:
He arrived at the right time to catch the train.
This could mean he arrived within the normal range of minutes before the train departed, in order to not miss the train.
Normally however, to distinguish between the two - a sense of urgency or other context is provided, consider the difference:
He arrived just in time for the train.
Here it is clear the person arrived at the last possible chance to catch the train.
Here are some more examples for on time:
- He arrived exactly on time for the train.
- He was always on time for meetings.
- He was never on time for meetings.
However, as Sven mentioned in their comment, this is just one of many ways you can use the phrases.