Problem: Sentence1: Their angry expressions were a clear sign they didn't want to talk.
Sentence2: Those clouds show little sign of raining soon.
Q: Does the term sign mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: A channel is typically what you rent from a telephone company.
Sentence2: The English Channel lies between France and England.
Q: Does the term channel mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: The foot of the list.
Sentence2: He stood at the foot of the tower.
Q: Does the term foot mean the same thing in both these sentences?

Answer: different meanings

Problem: Sentence1: He was a great actor in his time.
Sentence2: He waited a long time.
Q: Does the term time mean the same thing in both these sentences?

Answer:
the same meaning