hairdressing vs combing

hairdressing and combing both are nouns.

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

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

hairdressing: 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 hairdressing include brush, brushing, comb, shampoo, hairweaving.

hairdressing (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
a toiletry for the hair