vulgarism vs inelegance

vulgarism and inelegance both are nouns.

Word	Noun	Adjective	Verb	Adverb
vulgarism	Yes	No	No	No
inelegance	Yes	No	No	No

As nouns, inelegance is a hypernym of vulgarism; that is, inelegance is a word with a broader meaning than vulgarism:

vulgarism (noun)	inelegance (noun)
the quality of lacking taste and refinement	the quality of lacking refinement and good taste
an offensive or indecent word or phrase