hair care vs combing

hair care and combing both are nouns.

Word	Noun	Adjective	Verb	Adverb
hair care	Yes	No	No	No
combing	Yes	No	No	No

As nouns, combing is a hyponym of hair care; that is, combing is a word with a more specific, narrower meaning than hair care:

hair care: care for the hair: the activity of washing or cutting or curling or arranging the hair
combing: the act of drawing a comb through hair

Other hyponyms of hair care include brush, brushing, comb, shampoo, hairweaving.

hair care (noun)	combing (noun)
care for the hair: the activity of washing or cutting or curling or arranging the hair	the act of drawing a comb through hair