I always thought that the historical use of the name "midtown" was for the New Center area. So I have long assumed that the current use of Midtown included not only the Corridor, Brush Park [[aka Paradise Valley), and the Med Center, WSU, and Cultural Center areas, but also the New Center as well. At the very least it seems to me that name must include everything inside the north-of-downtown freeway rectangle.

Although, per Honky Tonk's response, certain areas along Third still seem a whole lot more Corridor than Midtown.