Myth: a cocoon and a chrysalis are the same thing.  In fact, the chrysalis is a butterfly pupa, which is a hard skin which appears after the caterpillar’s final shedding of its skin when it’s attached to a leaf via a silk pad spun by the caterpillar.  A cocoon is just a constructed silk casing used by moths and certain other types of insects.

Sources and other interesting moth and butterfly facts