hairstyle vs hairdo

hairstyle and hairdo both are nouns.

Word	Noun	Adjective	Verb	Adverb
hairstyle	Yes	No	No	No
hairdo	Yes	No	No	No

As nouns, hairstyle and hairdo are synonyms defined as:

hairstyle and hairdo: the arrangement of the hair (especially a woman's hair)

Other synonyms of hairstyle include coif, coiffure, hair style.

hairstyle (noun)	hairdo (noun)
the arrangement of the hair (especially a woman's hair)	the arrangement of the hair (especially a woman's hair)