midwestern United States vs middle west

midwestern United States and middle west both are nouns.

Word	Noun	Adjective	Verb	Adverb
midwestern United States	Yes	No	No	No
middle west	Yes	No	No	No

As nouns, midwestern United States and middle west are synonyms defined as:

midwestern United States and middle west: the north central region of the United States (sometimes called the heartland or the breadbasket of America)

Other synonyms of midwestern United States include Midwest.

midwestern United States (noun)	middle west (noun)
the north central region of the United States (sometimes called the heartland or the breadbasket of America)	the north central region of the United States (sometimes called the heartland or the breadbasket of America)