Question: Here is one sentence: I'll offset the time difference locally.
Here is another sentence: To offset one charge against another.
Does the offset mean the same thing in the two sentences?

Answer: the same meaning

Question: Here is one sentence: Open the door a crack.
Here is another sentence: There was a crack in the mirror.
Does the crack mean the same thing in the two sentences?

Answer: different meanings

Question: Here is one sentence: A remarkable degree of frankness.
Here is another sentence: There are 360 degrees in a circle.
Does the degree mean the same thing in the two sentences?

Answer: different meanings

Question: Here is one sentence: Answer the telephone.
Here is another sentence: Answer the door.
Does the answer mean the same thing in the two sentences?

Answer:
the same meaning