Of all the ones I've owned or worked on...
"Special" models are made of plastic and are similar if not identical to Brilharts, Selmer Goldentone, etc. Straight sidewalls that squeeze at the throat. Slight rollover baffle.
"Artist" models are made of hard rubber - which is to say there is some noticeable amount of sulfur in the compound. These have sidewalls that are mostly straight - perhaps slightly concave, but not significantly. Round throat which is medium to large, but not as large as Tone Edge Links. If the facing designation has a *R suffix, then it has a full size body. *S facing suffix indicates it is streamlined, so it is narrower like a metal, though the beak still has some appreciable height to it. If the facing number has a J prefix, that means there is a high step baffle. So you can find these pieces as "4*R" or "6*S" or "J7*R" or "J9*S" for example.
The Herbert Couf Special are also plastic, but there are Herbert Couf Artist models that are hard rubber. Some of these models are also streamlined but do not have a *S suffix, necessarily - sometimes just called "4*". The conventions changed over time, though I do not have a timeline to be specific about what changed when. Just that I've seen many variations.
I happen to have a Herbert Couf Special for alto which is clear plastic.
There are also Couf metal mouthpeices, by the way. They appear to me to be similar to Wagner metal mouthpieces. Silver plated brass.
I have not seen a plastic "Artist" model nor a "Special" in hard rubber - not to say they don't exist.
I don't collect many mouthpieces for collecting sake, but I have a thing for Coufs.