Problem: Sentence1: He sacrificed a piece to get a strategic advantage.
Sentence2: He needed a piece of granite.
Q: Does the term piece mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: She's my love, my life.
Sentence2: He could no longer cope with the complexities of life.
Q: Does the term life mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: She walked to a point where she could survey the whole street.
Sentence2: He held me up at the point of a gun.
Q: Does the term point mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: It will pay to wait.
Sentence2: It pays to go through the trouble.
Q: Does the term pay mean the same thing in both these sentences?

Answer:
the same meaning