hair oil vs hairdressing

hair oil and hairdressing both are nouns.

Word	Noun	Adjective	Verb	Adverb
hair oil	Yes	No	No	No
hairdressing	Yes	No	No	No

As nouns, hair oil and hairdressing are synonyms defined as:

Other synonyms of hair oil include hair grease, hair tonic.

hair oil (noun)	hairdressing (noun)
a toiletry for the hair	care for the hair: the activity of washing or cutting or curling or arranging the hair
	a toiletry for the hair