According to the Osprey book the Stug hull was based on the Panzer III hull,but was essentially it's own design.
Panzer III hulls were also used to speed up production of the Stug by putting the superstructure of the Stug III onto it.
A photo in the Osprey book shows a Stug with the stepped fenders and the caption decribes it as being one of the Panzer III hulled Sturmgeshutz.
Obviously there are differences between the lower hulls of the Stug and the Panzer,one of them being the splash guard at the front of the fender.The Stug's is short and fixed whereas the Panzer's is longer and hinged,as in your photo.

Steve.