Problem: Sentence1: Spoke a good word in his friend's behalf.
Sentence2: In your behalf.
Q: Does the term behalf mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: In the interest of safety.
Sentence2: Victorian furniture is an interest of mine.
Q: Does the term interest mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: He hit a home run.
Sentence2: The movie hits theaters in December.
Q: Does the term hit mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: Check into the rumor.
Sentence2: Check the brakes.
Q: Does the term check mean the same thing in both these sentences?

Answer:
different meanings