The wolf cut and the shag: the hero haircuts of now.
Are they the same thing?
Short answer: no.
To the layman's eye, they look very similar.
So what IS the difference?
The shag has cropped layers that frame the face to create volume. The key to emphasising the shag is a good set of bangs - particularly suited to a curtain bang, blended into the layers around the face. The shag also maintains a lot more volume around the face, which is a key difference that sets it apart.
The wolf cut doesn't actually have an exact sort of definitive shape. It is basically a combo of choppy and short layers, starting from around the crown of the head, cascading from front to back. Layering around the face, gradually getting thicker around the back with longer base layer will create a bit of a mullet effect, intentionally.
But the confusing thing here is that the wolf cut can be long OR short.