The .375 Winchester came along with the .356 and .307 Winchester cartridges when Winchester introduced their Big Bore '94 version of the lever action Winchester 94. You may already know all this.
As far as a parent cartridge goes ...? Well, it is about a tenth of an inch shorter than the .38/55 buffalo rifle cartridge. I have used .375 cases in my .38/55. Other way around won't work and of course, one must not shoot modern .375 loads in vintage .38/55s. Danger, Will Robinson!
Here is a crazy project a friend of mine and I did ... !
Necked down .375 brass to .357 for loading a wildcat: full length .30-30 Ack Imp chamber into a .357 barrel blank on an H&R single shot action. It's my hog gun. Neck is about .400 long. Not much of a shoulder though.
Resize/deprime with a .30-30 Ack Imp die for the body. Resize neck and seat bullets with .357 dies.
Crazy, but fun!