There is rampant misuse of the term “crusher cap” in reference to US visor caps in the WWII militaria collecting market. A crusher cap is a type of visor cap that is intended to be soft and pliable. Germans also had a crusher cap designed for field use, but that is another topic. US crusher caps were designed for pilots and air personnel to comfortably wear under their headset.
The distinguishing feature of a crusher cap is that the bill is made from a single layer of leather with a leather bead around it. Other visor caps typically have two layers of leather fused or sewn together, with a machine-stitched brim. A double ply visor stiffens the cap, making it less than ideal for wearing with a headset.
The quintessential US crushers coveted by collectors are Bancroft “Flighter” caps, offered in both tan and dark green wool. Luxembergs and Flight Weights are also desirable.
If you surf the net looking for a crusher, you will find a lot of mislabeled visor caps. True crushers command many times more money than even the nicest regular visors, so when you are buying a crusher cap, make sure you are actually buying a true crusher and not an overpriced visor cap.
Here are pics of a Bancroft Flighter from my collection that is part of an 8th Army Air Corps Bombardier group. Notice the single ply brim and relaxed shape.