I was trying to say what if those cals were known as "45 short" and "45 long" ONLY and no one really cared one was S&W and one Colt.
There were three different cartridges of differing lengths, so simply using short and long wouldn't be sufficient to distinguish them all.
I think they called them by what they were marked with the addition of any adjectives required to distinguish between different cartridges with similar markings.
As an example, nobody, these days, gets confused and calls the .38Special the .357Magnum Short, or the .38S&W the .38 Special Short. They call them what they're marked and then add on whatever adjectives they need to explain completely what they want.