Are marigolds chrysanthemums

Apparently, both marigolds and chrysanthemums are members of the daisy family (Asteraceae).

It depends what Marigold you mean. Calendula officinalis is the Pot Marigold the flower most commonly known as the Marigold. However the Corn Marigold is Chrysanthemum segatum this shows the problem of using common names to identify different plants.