IAN an orthopod.
I think Schultergelenkorthese covers several different types of shoulder brace/bandage, not all intended for the same purpose.
A “sling and swathe” is a particular technique, consisting of two parts – the sling to support the forearm, and the swathe round the body to keep the arm in the correct position.
First aid extremity splinting – sling and swathe with two triangular bandages:
More sophisticated commercial sling and swathe braces still have the two components – the sling support and a section round the body – but there are many variations on the theme now in use.
As well as being called Schulter(gelenk)orthese, I’ve also seen these referred to as Schulterfixationbandage