Problem: Sentence1: Raise a smile.
Sentence2: Chew with your mouth shut -- were you raised in a barn?
Q: Does the term raise mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: Your header is too long; "Local Cannibals" will suffice.
Sentence2: He took a header into the shrubbery.
Q: Does the term header mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: You really have to empathize with their doing it.
Sentence2: You really have to empathize with them.
Q: Does the term empathize mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: Book fair.
Sentence2: World fair.
Q: Does the term fair mean the same thing in both these sentences?

Answer:
the same meaning