middle west vs midwestern United States

middle west and midwestern United States both are nouns.

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

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

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

Other synonyms of middle west include Midwest.

middle west (noun)	midwestern United States (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)