side dish vs side order

side dish and side order both are nouns.

Word	Noun	Adjective	Verb	Adverb
side dish	Yes	No	No	No
side order	Yes	No	No	No

As nouns, side dish and side order are synonyms defined as:

side dish and side order: a dish that is served with, but is subordinate to, a main course

Other synonyms of side dish include entremets.

side dish (noun)	side order (noun)
a dish that is served with, but is subordinate to, a main course	a dish that is served with, but is subordinate to, a main course