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

If you were in my place what would you do?

He comes from a place near Chicago.

A: different meanings

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

His state of health.

The current state of knowledge.

A: the same meaning

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

He's just been released from Shadwell nick prison after doing ten years for attempted murder.

He was arrested and taken down to Sun Hill nick police station to be charged.

A:
the same meaning