.32 Wadcutter should indeed be .32 S&W Long. Has been a favorite for target shooting in Europe for decades. The Fiocchi .32 Wadcutter ammo has a headstanp that says exactly ".32 Wadcutter" and doesn't actually say .32 S&W Long, but by dimension, it certainly is.
I've heard discussion claiming the .38 Special brass that was originally sold as ammo with the 148gr hollow base wadcutter bullet is different internally than typical .38 Special brass but I can also say that I don't use any wadcutter specific brass for my S&W Model 52's, all of which are highly capable and extremely accurate pistols.
But I toss that out there anyway as perhaps the .32 Wadcutter brass is different than .32 S&W Long brass. I have a slew of both, and apologies as I have no interest whatsoever in trying to determine if the case capacity is much, if any different.
The European and Euro style .32 Wadcutter guns are pistols such as the Walther GSP, Sig P240, Benelli MP-95, Pardini HP, etc.
I'm fortunate to own a Walther GSP-c from the 80's and it's chambered for the .32 Wadcutter. It's a joy to shoot. And as a funny side note, the magazine is not in the grip but is forward of it, and because of this... the gangly 5-shot .32 Wadcutter pistol is recognized as an "ASSAULT PISTOL" by the State of New York and Cook County, IL, two places that I have no plans to visit with it.