Michael Swans excellent Practical English Usage (Oxford University Press), provides a succinct answer to both of these questions: "On time = at the planned time; neither late nor early:
Peter wants the meeting to start exactly on time.
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In time = with enough time to spare; before the last moment:
He would have died if they hadnt got him to the hospital in time." p. 450
Jibu nililitoa muda mrefu baada ya kuona watu hawatoi msaada:
ontime=exactly on the time arranged
intime=just before the time arranged(na siyo baada ya muda)
It is always good to arrive for appointments in time.
"In time" is a range starting well before the appointment, and ending "on time". In other words the exact point of on time is the last point of the line of in time.