hair clip vs claw clip

hair clip and claw clip both are nouns.

Word	Noun	Adjective	Verb	Adverb
hair clip	Yes	No	No	No
claw clip	Yes	No	No	No

As nouns, claw clip is a hyponym of hair clip; that is, claw clip is a word with a more specific, narrower meaning than hair clip:

hair clip: any of various clasps and clips used for holding hair in place.
claw clip: a type of hair clip with interlocking teeth connected by a spring

Other hyponyms of hair clip include hair slide, hair clamp, hair claw.

hair clip (noun)	claw clip (noun)
any of various clasps and clips used for holding hair in place.	a type of hair clip with interlocking teeth connected by a spring