Q: Does the word "cast" mean the same thing in "Who cast this beautiful movie?" and "Cast a vote."?

A: different meanings

Q: Does the word "field" mean the same thing in "The set of rational numbers, \mathbbQ, is the prototypical field." and "Field of view."?

A: different meanings

Q: Does the word "ping" mean the same thing in "Ping your machine in the office." and "The bugs pinged the lamp shade."?

A: different meanings

Q: Does the word "head" mean the same thing in "A head of cauliflower." and "A head of lettuce."?

A:
the same meaning