If you loaded the 44 Colt as it was originally made, a heel based 45 caliber bullet, or a hollow based 44 bullet, the 44 Colt chambering would work. As it is, the "modern" load for a 44 Colt is inside the case bullet, making it a 429 caliber like the 44Russian/Special/Magnum.
As mentioned by Quick Fire, the 44 Colt bore is .454, so it must be chambered for 45 Schofield or 45 Colt to work with that bore.
No doubt, having the boring and rifling tools set up in the Colt factory for the 1860 Army, the 45 SAA Colt was designed to use that bore from the get-go.