Q: Does the word "refine" mean the same thing in "Refine paper stock." and "Refine pig iron."?

A: the same meaning

Q: Does the word "rack" mean the same thing in "Rack one's brains." and "Rack a camera."?

A: different meanings

Q: Does the word "work" mean the same thing in "She knows how to work the system." and "Is your husband working again?"?

A: different meanings

Q: Does the word "sake" mean the same thing in "For your sake." and "Died for the sake of his country."?

A:
the same meaning