woolly vs woolly-headed

woolly and woolly-headed both are adjectives.

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

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

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

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

woolly (adjective)	woolly-headed (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