side dish vs mushy peas

side dish and mushy peas both are nouns.

Word	Noun	Adjective	Verb	Adverb
side dish	Yes	No	No	No
mushy peas	Yes	No	No	No

As nouns, mushy peas is a hyponym of side dish; that is, mushy peas is a word with a more specific, narrower meaning than side dish:

side dish: a dish that is served with, but is subordinate to, a main course
mushy peas: marrowfat peas that have been soaked overnight and then boiled; served with fish and chips

Other hyponyms of side dish include raita.

side dish (noun)	mushy peas (noun)
a dish that is served with, but is subordinate to, a main course	marrowfat peas that have been soaked overnight and then boiled; served with fish and chips