lower class vs social class

lower class and social class both are nouns.

Word	Noun	Adjective	Verb	Adverb
lower class	Yes	No	No	No
social class	Yes	No	No	No

As nouns, social class is a hypernym of lower class; that is, social class is a word with a broader meaning than lower class:

lower class: the social class lowest in the social hierarchy
social class: people having the same social, economic, or educational status

Other hypernyms of lower class include class, socio-economic class, stratum.

lower class (noun)	social class (noun)
the social class lowest in the social hierarchy	people having the same social, economic, or educational status