social class vs socio-economic class

social class and socio-economic class both are nouns.

Word	Noun	Adjective	Verb	Adverb
social class	Yes	No	No	No
socio-economic class	Yes	No	No	No

As nouns, social class and socio-economic class are synonyms defined as:

social class and socio-economic class: people having the same social, economic, or educational status

Other synonyms of social class include class, stratum.

social class (noun)	socio-economic class (noun)
people having the same social, economic, or educational status	people having the same social, economic, or educational status