I’ve owned a Remington 32 and a San Remo Grade Krieghoff 32. Both were trap guns. The Krieghoff 32 had the blood red stock that you allude to. The Remington 32 is older than the Krieghoff; it’s pre-war. They are very similar guns but the Krieghoff is not a copy of the Remington, particularly the internals.
The Krieghoff 32 is a very nice gun and not in the least inferior to the more modern K-80(which I also own at present).