Q: Does the word "break" mean the same thing in "I don't know how to break this to you, but your cat is not coming back." and "News of her death broke in the morning."?

A: the same meaning

Q: Does the word "take" mean the same thing in "Tomorrow the doctor will take the cast off her arm." and "Can you take this bag, please."?

A: different meanings

Q: Does the word "tomorrow" mean the same thing in "Everyone hopes for a better tomorrow." and "Tomorrow's world."?

A: the same meaning

Q: Does the word "death" mean the same thing in "The death of my grandmother saddened the whole family." and "Her death came as a terrible shock."?

A:
the same meaning