muffin case vs muffin cup

muffin case and muffin cup both are nouns.

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

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

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

muffin case (noun)	muffin cup (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.