Midwest is generally referred to as those state which once made up the Northwest Territories and include Ohio, Indiana, Michigan, Illinois, Wisconsin and Minnesota. Iowa and Missouri are also included on occasion.
"West" is generally referred to those states along and west of the Rocky Mountains. The states in between the "Midwest" and "West" are commonly referred to as Plains States.
These are generic terms and there are no hard-and-fast rules as to what state falls into which category.