hair care vs brushing

hair care and brushing both are nouns.

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

As nouns, brushing is a hyponym of hair care; that is, brushing 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
brushing: the act of brushing your hair

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

hair care (noun)	brushing (noun)
care for the hair: the activity of washing or cutting or curling or arranging the hair	the act of brushing your hair
	the act of brushing your teeth