Q: Does "toy" have the same meaning in the following two sentences?

To toy with a piece of food on one's plate.

Toy with an idea.

A: the same meaning

Q: Does "mail" have the same meaning in the following two sentences?

He works for the United States mail service.

The mail handles billions of items every day.

A: the same meaning

Q: Does "cut" have the same meaning in the following two sentences?

Cut the engine.

She cut all of her major titles again.

A:
different meanings