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

The rate of production at the factory is skyrocketing.

He works at a great rate.

A: the same meaning

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

I wish I had seen the look on his face when he got the news.

He looked out at a roomful of faces.

A: different meanings

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

A trial of progesterone failed to relieve the pain.

A sample for ten days free trial.

A:
the same meaning