muffin cup vs muffin case

muffin cup and muffin case both are nouns.

Word	Noun	Adjective	Verb	Adverb
muffin cup	Yes	No	No	No
muffin case	Yes	No	No	No

As nouns, muffin cup and muffin case are synonyms defined as:

muffin cup and muffin case: a round sheet of paper, foil, or silicone with scallop-pressed edges, giving the muffin a round cup shape.

muffin cup (noun)	muffin case (noun)
a round sheet of paper, foil, or silicone with scallop-pressed edges, giving the muffin a round cup shape.	a round sheet of paper, foil, or silicone with scallop-pressed edges, giving the muffin a round cup shape.