tooth socket vs socket

tooth socket and socket both are nouns.

Word	Noun	Adjective	Verb	Adverb
tooth socket	Yes	No	No	No
socket	Yes	No	No	No

As nouns, socket is a hypernym of tooth socket; that is, socket is a word with a broader meaning than tooth socket:

tooth socket (noun)	socket (noun)
a bony socket in the alveolar ridge that holds a tooth	a receptacle into which an electric device can be inserted
	receptacle where something (a pipe or probe or end of a bone) is inserted
	a bony hollow into which a structure fits