hair clamp vs hair clip

hair clamp and hair clip both are nouns.

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

As nouns, hair clip is a hypernym of hair clamp; that is, hair clip is a word with a broader meaning than hair clamp:

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

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