lower-case letter vs grapheme

lower-case letter and grapheme both are nouns.

Word	Noun	Adjective	Verb	Adverb
lower-case letter	Yes	No	No	No
grapheme	Yes	No	No	No

As nouns, grapheme is a hypernym of lower-case letter; that is, grapheme is a word with a broader meaning than lower-case letter:

lower-case letter: 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 lower-case letter include character, graph, graphic symbol.

lower-case letter (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