Q: Does the word "sake" mean the same thing in "For your sake." and "Died for the sake of his country."?

A: the same meaning

Q: Does the word "spin" mean the same thing in "One of the planet's moons has a slower spin than the others." and "He took the new car for a spin."?

A: different meanings

Q: Does the word "shoot" mean the same thing in "Shoot a movie." and "Shoot a basket."?

A: different meanings

Q: Does the word "take" mean the same thing in "Tomorrow the doctor will take the cast off her arm." and "The test grader takes off a point for every misspelled word."?

A:
the same meaning