Your question points out a problem with the definitions. The labels for American regions is hopelessly out of date. I am talking about the ones used by the US Census Bureau. The original regional definitions have next to nothing in common with 21st century realities. Probably the only one which still fits is New England. Example of poorly defined area: Texas and Oklahoma are labeled Southern by the Census Bureau, but New Mexico and Arizona are labeled West. West covers more than a third of the US and includes states from New Mexico to Hawaii. New Mexico and Arizona have far more in common with states like Texas or Oklahoma, than they do with Washington, Oregon, California or Hawaii. Personally, I think more regions are in order.
Deep South is an unofficial term which is usually defined as Louisiana eastward to the Georgia coast. In defining regions more rationally, I would label Louisiana and Arkansas east to the Atlantic Coast and as far north as Kentucky, inclusive, as Southeast. I would label Arizona, New Mexico, Oklahoma and Texas as Southwest. I might add Delaware and Maryland to the Mid-Atlantic region as they have more in common with that region. I would call California, Oregon, Washington, Alaska and Hawaii the Pacific region. I would consider splitting the Midwest and have the Plains states (Kansas, Nebraska, and the Dakotas) as separate from places such as Ohio, Michigan, Illinois, Iowa, etc which would remain Midwest. I would label Nevada to Colorado inclusive, north to Montana and Idaho as Intermountain West.
Anyway, my two cents.