sought after vs sought-after

sought after and sought-after both are adjectives.

Word	Noun	Adjective	Verb	Adverb
sought after	No	Yes	No	No
sought-after	No	Yes	No	No

As adjectives, sought after and sought-after are synonyms defined as:

Other synonyms of sought after include coveted, in demand.

sought after (adjective)	sought-after (adjective)
much wanted	much wanted
	being searched for