There was a short 45 Colt, see below.
But the history of our language is so riddled with misnomers it can drive you crazy if you let it! The 45 Colt vs. 45 Long Colt certainly is a common one especially among knowledgeable gun people.
History of the unofficial 45 Long Colt description:
As soon as those unaware of the 'short' 45 Colt, learn of its existence, the discussion can end.
Although there was initially a justification for the long 45 Colt description, it preceded the short 45 Colt Rem-UMC round by decades.
Shortly after the Army procured S&W Schofield revolvers, the 1st time a supply depot accidentally shipped 45 Colt ammo to a unit issued the 45 S&W Schofield revolvers (needing the shorter S&W round), the Army figured out it had a multiple ammunition problem! Coincidentally troops were complaining about the recoil of the original Colt ~40gr load of blackpowder and resulting poor marksmanship.
Soon the original ~40gr load was reduced to 28 grs. Then government arsenals established the 45 S&W round as standard in 1887 since it would chamber in both the 45 Colt SAA and S&W revolvers.
Since the 45 Colt cartridge inventory was not depleted for some time, those troopers who appreciated the superior performance of the 45 Colt round and were issued the 45 Colt SAA, specifically requested the longer round, the “long Colt” round with small L.
Remington-UMC did actually introduce a “short” 45 Colt round before WW I. It’s not a Remington version of the 45 Schofield because it has a narrower and thicker rim like the 45 Colt and will not chamber in S&W Schofield revolvers.
It’s simply head-stamped 45 Colt. It’s of similar length to the Schofield round but is not the same as the Schofield round because it has the standard, small 45 Colt rim size. It does not properly extract from the Schofield revolvers. I have several factory loaded rounds and cases which are balloon head cases. The headstamps of the Remington short 45 Colt and the 45 Schofield were always different to delineate their lack of interchangeability in S&W revolvers.
Colt also developed the 45 ACP in the 1905 model. They used the long colt terminology to keep people from buying the wrong ammo for their semi-autos.
And there you have it; it was originally a description, NOT an official designation. Since both revolvers were popular on the frontier the distinguishing description continued to be used whenever ammunition was purchased. SAA users wanted the 45 Colt rounds. As is the case with most misnomers, the darned term stuck. So much so that some ammunition in 45 Colt caliber is actually marked 45 LC on packaging boxes, and is to this day by several manufacturers. I’ve become indifferent to either term.
But I just don't see the need for continuing to use the obsolete term 45 'LONG' Colt any longer.
There were no original guns even marked as such, certainly not COLT SAAs! I've only seen a few of the modern era SAA clones marked 45 Long Colt.
But again, I don't lose any sleep over it either way.