Long ago and far away, I went to the Jacobs website to investigate whether a Jacobs Rambrake on a 5.9 Cummins could reasonably be called a "Jake Brake".
On that Jacobs website homepage, JACOBS identified the Rambrake exhaust brake as installed on the 5.9 Cummins in a Dodge pickup as a "JAKE BRAKE".
IMO, if it is good enough for the manufacturer, it is good enough for me.
The Jacobs Rambrake that was on my old 1994 Dodge 3500 CTD actually was a Jake Brake.
The Jacobs company said so!
I suspect the OP has a compression brake, since I have never heard of nor seen a 2-stage exhaust brake. Whether it is actually a real Jake Brake or merely a jake-brake type system I don't know.