The difference:

These thumb rests are virtually the same.
Only one part is different and that is the casing which can be turned to the left and right.

We where asked to make a thumb rest especially for the double reed market.

The "Oboe" thumb rest has a casing already machined at an angle, whereas the hollow cavity of the Maestro is machined straight and has to be adjusted
more to the left when used on an Oboe (as when used on a clarinet).

This is because the diameter of the body of the Oboe is quite smaller than of the Clarinet.
The thumb points to the index finger at a sharper angle on the Oboe.

Note

When only a Maestro thumb rest is availlable you could use this thumb rest as well. (if you do not mind that there is a Clarinet on the box)