Q: Does the word "staple" mean the same thing in "Tow is flax with short staple." and "Staple fibers vary widely in length."?

A: the same meaning

Q: Does the word "backup" mean the same thing in "After the power failure, we had to restore the database from backup." and "He made a backup in case the original was accidentally damaged or erased."?

A: the same meaning

Q: Does the word "trust" mean the same thing in "Don't trust my ex-wife." and "I trust you will behave better from now on."?

A: different meanings

Q: Does the word "part" mean the same thing in "She played the part of Desdemona." and "We all have a part to play."?

A:
the same meaning