As has already been pointed out in the comments, the US Army Air Force was actually a combat branch of the US Army. It originally was called the Air Corps, but then became known as the US Army Air Force in 1942. It had it's own commander who reported to the Chief of Staff of the Army. Since this was officially a branch of the US Army, the ranks that were distributed at that time were still US Army ranks. That means that your grandfather's rank would have been that of a Staff Sergeant, E-6.
The branch of the military currently know as the US Air Force didn't come into existence until 1947. At that time, they established their own rank hierarchy and introduced ranks that identified their servicemen as different levels of "Airman" (even though most people of this rank never actually spent any time in the air). The Staff Sergeant rank in the USAF is designated as an E-5, with the E-6 designation becoming the Technical Sergeant.