lowercase vs grapheme

lowercase and grapheme both are nouns.

Word	Noun	Adjective	Verb	Adverb
lowercase	Yes	Yes	No	No
grapheme	Yes	No	No	No

As nouns, grapheme is a hypernym of lowercase; that is, grapheme is a word with a broader meaning than lowercase:

lowercase: the characters that were once kept in bottom half of a compositor's type case
grapheme: a written symbol that is used to represent speech

Other hypernyms of lowercase include character, graph, graphic symbol.

lowercase (noun)	grapheme (noun)
the characters that were once kept in bottom half of a compositor's type case	a written symbol that is used to represent speech

lowercase (adjective)	grapheme (adjective)
relating to small (not capitalized) letters that were kept in the lower half of a compositor's type case