The Difference Betweeen "in time" and "on time"

These are some common doubts that many students (even advanced ones) have. Let's elicit them once and for all:

On time = at the planned time; neither late nor early:
- Dean wants the meeting to start exactly on time.
- Elisa hates being late. She always arrives on time.

In time = with enough time to spare; before the last moment:
- She would have died if they hadn’t called the paramedics in time.
- Unfortunately, I didn't arrive in time. My friend had already taken the plane.