working class vs social class

working class and social class both are nouns.

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

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

working class: a social class comprising those who do manual labor or work for wages
social class: people having the same social, economic, or educational status

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

working class (noun)	social class (noun)
a social class comprising those who do manual labor or work for wages	people having the same social, economic, or educational status