Yes, the internals of the adapter are designed/rated to only be used with that 20A equipment, but be able to plug into a typical welder circuit, which will have a 50A configuration regardless of OPCD, which are commonly 50A, but sometimes only 30A.
The power supply cord for the machine is also probably only #14, even though some are 20A or even 30A.
I have that same adapter with my Hobart 160i that I Beta-tested a few years ago.