crescent vs crescent-shaped

crescent is a noun but crescent-shaped is not a noun.

Word	Noun	Adjective	Verb	Adverb
crescent	Yes	Yes	No	No
crescent-shaped	No	Yes	No	No

As adjectives, crescent and crescent-shaped are synonyms defined as:

Other synonyms of crescent include lunate, semilunar.

crescent (noun)	crescent-shaped (noun)
any shape resembling the curved shape of the moon in its first or last quarters

crescent (adjective)	crescent-shaped (adjective)
resembling the new moon in shape	resembling the new moon in shape