Nonmenclature....
I think the OPs question was answered ad infinitum, lots of interesting explanations and opinions,
I chuckled a bit being that flundertaker has been here since 2013 and almost wondered if he wanted to stir the pot a tiny bit lol.
But the discussion reminded me of a thread years ago, I had acquired a Combat Magnum that IIRC had a serial and ship date that should have put it into the range of Model number guns but it did not have one stamped in the yoke cut, I referred to it as a "Pre 19" at the time, my friend Chris SNW19 pmd me and we got into an interesting discussion on the topic,
In the end he suggested that it might be better to refer to that gun as a "Non model marked Model 19" to which I agreed, btw IIRC the factory designation for that model was KT357 , I could be wrong I'm getting old.
The N Target frame .357 has more history and as such more nuances, while there are no 5 screw Combat Magnums there are 4 and 5 screw N Target frame .357's.
Can't recall if the SW ads and box's all say "The .357 Magnum" or if some say "The S&W .357 Magnum", it suffices to say the NT357 was the only .357 SW offered up until the introduction of the "Highway Patrolman" ( maybe the quotation marks go outside the "the"?).
If "The" is actually part of the name it gets real confusing like who's on first kinda thing,
Man walks into gun store in 1956, I wanna buy the SW .357 Magnum I was looking at last week, which one? The S&W .357 Magnum, ... oh you mean this one with the fancy checkered top? No the other S&W .357 Magnum the 4" one, Do you mean the Combat Magnum? No the cheaper one with the smooth top....oh the Highway Patrolman?
Model numbers made that easier, they also enabled us to ping the guns era, imagine if no Model number system existed you'd be saying I have a Combat Magnum dash 3.
It's confusing enough that SW revived the old name M&P and applies it to their various handguns and rifles in various calibers.
I try not to get hung up on the whole pre model stuff, especially if you add how many screws it has and what year it's from or add the name so we are on the same page.
If someone says "I have a four inch, four screw SW .357 Magnum that shipped around 1956-57", my next question will be ... Which model?