Problem: Sentence1: There was no food in the house, so I had to remain hungry.
Sentence2: There remains the question of who pulled the trigger.
Q: Does the term remain mean the same thing in both these sentences?

Answer: different meanings

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: They gained ground step by step.
Sentence2: They fought to regain the lost ground.
Q: Does the term ground mean the same thing in both these sentences?

Answer: the same meaning

Problem: Sentence1: The crowd had to run away from the burning structure with only the clothes on their backs.
Sentence2: She ran her fingers along the carved figurine.
Q: Does the term run mean the same thing in both these sentences?

Answer:
different meanings