box spring vs bedspring

box spring and bedspring both are nouns.

Word	Noun	Adjective	Verb	Adverb
box spring	Yes	No	No	No
bedspring	Yes	No	No	No

As nouns, bedspring is a hypernym of box spring; that is, bedspring is a word with a broader meaning than box spring:

box spring: a coiled bedspring in a frame that is covered with cloth
bedspring: (usually in the plural) one of the springs holding up the mattress of a bed

box spring (noun)	bedspring (noun)
a coiled bedspring in a frame that is covered with cloth	(usually in the plural) one of the springs holding up the mattress of a bed