Smith doesn't seem, to me, to have had a problem with that. They marked their 32/20 M&Ps as "32 Winchester".
Colt didn't like it. "We will not put 38 Smith & Wesson on our revolvers! That cartridge is now a 38 Colt New Police!!!!" Oooookay
I've also heard that Marlin did not like it. That's why we have the 30/30, and the 44/40. Because Marlin did not want to put 30 WINCHESTER centerfire and 44 WINCHESTER centerfire on their guns.
But there was one pistol maker - Merwin and Hubert?? Something like that - that just marked their pistols "Winchester rifle cartridge".
Smith & Wesson didn't have a problem because Winchester was not a competitor. The .30-30 and .44-40 cartridge designations indicated caliber and powder charge weight.
I see a lot more evidence of an "us or them" attitude before WWII. Colt didn't even make a double action .45 Colt by the time of the S&W 25-5. They'd lost the large frame revolver war, and badly.
Things seem to have come full circle...I'm much more interested in an Anaconda in .45 Colt than even the current no-IL MGs, and even if one were offered in the same caliber.