You now offer new information that can make a huge difference. If it belonged to a TC employee, it could very easily be a "lunch time" special barrel... IOW something made by the employee not offered standard production by TC. Your comment it is marked 375 TC only suggests that is very possible also, but not what cartridge it is for sure - "something" already out there, something they wildcatted themselves.
Should be easy enough to tell the difference between a 375 Win and 375SM chamber though, the later will be about 1/2" shorter. A chamber cast will verify what cartridge it is... but just measuring case head diameter and case length as best as you can probably would also.
The 375 Win is a modern version of an old Winchester black powder cartridge that Winchester came out with for a big bore lever rifle (sometime not too long after the mid 70's based on where I lived). Don't remember which old BP cartridge off hand for sure, but probably from the 38-55 Win. TC didn't add it to their standard production barrels until maybe early 90's if I remember from about when I got one to try it out. I usually tried whatever they made new for the Contender's soon after they came out with them IOW.
The 375 Super Mag is a Gates wildcat from sometime in the late 70's/early 80's based on a 30-30 Win case. Was probably about mid-late 80's when I first shot it in a buddies DW revolver. TC never offered it as a standard production barrel that I remember, can't remember if they ever did from their so called custom shop.
Just a lot of guess work until you verify what the barrel is chambered for. Maybe some of it will help you.
