My memory is that the Colt Three Fifty-Seven (as Colt called it in their advertising) and the Colt Trooper are different guns.
The Three-Fifty-Seven came out in 1953 or '54, anyway predating the Python by one year. It was the first frame mounted centerfire revolver. With the exception of the barrel profile — with the vented rib and underlug of the Python — the Python and the 3-5-7 are identical in their extensively hand fitted and tuned internals.
The early Troopers, in .38 and .22 only, had hammer mounted firing pins. They did not have the extensively hand-fitted internals of the Python and the 3-5-7.
The Three-Fifty-Seven was intended to be Colt's premier revolver but it was surpassed, at least in Colt's marketing, by the introduction of the Python a year later, becoming sort of the "odd man out" in Colt's line up.
In the early 60s, 1961 IIRC, the 3-5-7 ceased production, the Trooper firing pin moved to frame mounted, and a .357 Trooper was introduced. Again, the Trooper never had the extensive hand fitting of the Python or Three Fifty-Seven.
While identical in outward appearance, except for barrel lettering, they are different guns.
At least that is how I recall the history from back when I was collecting Colts for several years.
