Problem: Sentence1: We beat the competition.
Sentence2: Agassi beat Becker in the tennis championship.
Q: Does the term beat mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: Home is where the heart is.
Sentence2: There's no place like home.
Q: Does the term home mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: It may rain in which case the picnic will be canceled.
Sentence2: Latin has six cases, and remnants of a seventh.
Q: Does the term case mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: The process of calcification begins later for boys than for girls.
Sentence2: Events now in process.
Q: Does the term process mean the same thing in both these sentences?

Answer:
the same meaning