Midwest vs middle west

Midwest and middle west both are nouns.

Word	Noun	Adjective	Verb	Adverb
Midwest	Yes	No	No	No
middle west	Yes	No	No	No

As nouns, Midwest and middle west are synonyms defined as:

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

Other synonyms of Midwest include midwestern United States.

Midwest (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)