woolly-headed vs woolly

woolly-headed and woolly both are adjectives.

Word	Noun	Adjective	Verb	Adverb
woolly-headed	No	Yes	No	No
woolly	No	Yes	No	No

As adjectives, woolly-headed and woolly are synonyms defined as:

woolly-headed and woolly: confused and vague; used especially of thinking

Other synonyms of woolly-headed include addled, befuddled, muddled, muzzy, wooly-minded, wooly.

woolly-headed (adjective)	woolly (adjective)
confused and vague; used especially of thinking	confused and vague; used especially of thinking
	covered with dense often matted or curly hairs
	having a fluffy character or appearance
	covered with dense cottony hairs or hairlike filaments