lower-case letter vs graph

lower-case letter and graph both are nouns.

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

As nouns, graph is a hypernym of lower-case letter; that is, graph 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
graph: a written symbol that is used to represent speech

Other hypernyms of lower-case letter include character, grapheme, graphic symbol.

lower-case letter (noun)	graph (noun)
the characters that were once kept in bottom half of a compositor's type case	a visual representation of the relations between certain quantities, represented as points, plotted with reference to a set of axes
	a visual display of information
	a written symbol that is used to represent speech

lower-case letter (verb)	graph (verb)
	represent by means of a graph
	plot upon a graph