brushing vs hairdressing

brushing and hairdressing both are nouns.

Word	Noun	Adjective	Verb	Adverb
brushing	Yes	No	No	No
hairdressing	Yes	No	No	No

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

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

Other hypernyms of brushing include hair care, haircare.

brushing (noun)	hairdressing (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	a toiletry for the hair