Is a Morgan dollar the same size as a Kennedy half dollar?

Not at all. Remember, at one time the sizes of coins were proportional to their values so a Morgan dollar is (essentially) twice the size of a Kennedy half dollar.

Specifically, Morgan dollars are 38 mm in diameter and weigh 26.7 gm when new. JFK halves are 30 mm in diameter and weigh anywhere from 11.34 gm to 12.5 gm depending on their metal composition.