Q: Does the word "power" mean the same thing in "The power of his love saved her." and "The deterrent power of nuclear weapons."?

A: the same meaning

Q: Does the word "fit" mean the same thing in "A fit of coughing." and "I admired the fit of her coat."?

A: different meanings

Q: Does the word "catch" mean the same thing in "I have to stop for a moment and catch my breath." and "Catch one's breath."?

A: the same meaning

Q: Does the word "art" mean the same thing in "The art of conversation." and "How great thou art!"?

A:
the same meaning