Problem: Sentence1: During the firework display that ended the gala the noise reached 98 decibels.
Sentence2: He enjoyed the street noises.
Q: Does the term noise mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: For your sake.
Sentence2: Died for the sake of his country.
Q: Does the term sake mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: 200 head of cattle and 50 head of horses.
Sentence2: A head of steam.
Q: Does the term head mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: Unremitting pursuit of wealth doesn't bring happiness, particularly if successful.
Sentence2: The culprit started to run and the cop took off in pursuit.
Q: Does the term pursuit mean the same thing in both these sentences?

Answer:
the same meaning