brushing vs hair care

brushing and hair care both are nouns.

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

As nouns, hair care is a hypernym of brushing; that is, hair care is a word with a broader meaning than brushing:

brushing: the act of brushing your hair
hair care: care for the hair: the activity of washing or cutting or curling or arranging the hair

Other hypernyms of brushing include haircare, hairdressing.

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