Question: Here is one sentence: The set of all rational numbers is a field.
Here is another sentence: The set of rational numbers, \mathbbQ, is the prototypical field.
Does the field mean the same thing in the two sentences?

Answer: the same meaning

Question: Here is one sentence: The Union action of emancipating Southern slaves.
Here is another sentence: The United Nations must have the power to propose and organize action without being hobbled by irrelevant issues.
Does the action mean the same thing in the two sentences?

Answer: the same meaning

Question: Here is one sentence: The sweat cut little rivulets into her face.
Here is another sentence: Cut a movie scene.
Does the cut mean the same thing in the two sentences?

Answer: different meanings

Question: Here is one sentence: Education is the door to success.
Here is another sentence: I knocked on the vice president's door.
Does the door mean the same thing in the two sentences?

Answer:
different meanings