The phrase “on the phone” means that someone is using a telephone. The following examples show how “on the phone” is used:
- Please do not interrupt your mother while she is on the phone. [=while she is using the phone]
- Can you please turn down the TV? I am on the phone.
- He was on the phone when I arrived at his house so I let myself in.
The phrase “over the phone” means that something is done using the phone as a way to do it. The following examples show how “over the phone” is used:
- She told him the news over the phone. [=she used the phone to tell him the news rather than telling him in a letter or in person]
- I am able to pay my bills over the phone so I don’t have to write checks.
- We ordered take-out over the phone before driving to the restaurant to pick it up.
I hope this helps.