Hey guys.
I was told by folks at S&W that the 7-rd CS9 & original 7-rd 3913TSW mags differed only in the mag butt plate. (Same springs & followers, too.) The cutaway grip for the first 3913TSW model used a wider, fatter & shorter butt plate to conform to the grip.
Standard curved butt plate on the left and original 3913TSW plate on the right.
31913TSW butt plate on a mag in my CS9:
Standard curved plate on mag in CS9:
How much support for your fingers do you desire in the short CS9?
A friend who traded his original 3913TSW for a newer 3913TSW gave me a bunch of 7-rd mags from his older TSW, keeping just enough to have some extra for his CS9. He used to use them interchangeable in both his 7-shot guns (CS9 & original TSW) and I use them interchangeably in my CS9.
The CS45 is a bit of another story.
The difference in the mag bodies between the 6-rd 4513TSW and the CS45 is the presence of the extra set on indentations in the CS45 mag (which can sometimes make loading & unloading mags a bit of a chore). I was told that early in the model's production the engineers decided that the increased recoil of the CS45 really required a modification to the standard 6-rd mag body (which was used in the original 4513TSW with the cutaway grip profile). They felt that an extra set of indentations was needed to help prevent the top round from being displaced under recoil (which could cause feeding problems during cycling). The extra set of indentations in the CS45 mag bodies were intended to provide that balance of allowing the rounds to rise fast enough to provide proper feeding timing (helped along by the heavier recoil and inertia to some degree), but yet to keep the rounds from jumping forward out from under the lips due to the CS45's heavier recoil.
The mag springs are the same in the 6, 7 & 8-rd 3rd gen .45 mags, as are the followers.
The original 4513TSW mag butt plate was also wider and shorter than the standard curved one used on the later production 4513TSW & 457.
I've tried the 6-rd 4513TSW mags in my CS45 and experienced some repeated feeding issues. The problems involved instances where the rounds either were seemingly being released too soon and a nose-up stoppage occurred, or else the next round up (usually the last round) would actually jump free of the lips and be "ejected" with the empty, just-fired case. Annoying. This didn't happen a lot, but often enough that I stopped using them even for the range early on.
On the other hand, I recall trying the CS45 mags in my 4513TSW without a similar problem ... but that was many years ago and I've not repeated the experiment.
I've simply collected too many mags for the original 4513TSW to need to worry about trying to use the CS45 mags in that gun.

I've also got a few 7-rd .45 mags which I can use as spares in my older 4513TSW if needed. I have quite a lot of CS45 mags I've collected, too. I use the CS45 mags in the CS45 and the 4513TSW mags in the 4513TSW, for both range and carry roles. Easier for me that way.
Magazines are at the very heart of a semiauto pistol's optimal feeding and functioning. Why fool around with it if unnecessary?
The standard 6-rd 4513TSW mag is on the left in this picture and the CS45 is on the right:
A bit of trivia that might be interesting ...
I was talking to someone in Pistol Repair at the factory about the CS45 about the time they had just released it in stainless (because I'd just bought one and had to address an overly tight barrel tab in mine). I was told that they had decided the secondary set of indentations had been needed after the magazines had already been in production, and some existing mags had to have the extra set of indentations added by hand while the change was being made to incorporate them during production.
This adding of the second set of indentations by hand-stamping them in the bodies apparently resulted in a small number of the indentations being unevenly placed (in relative "height" to each other on each side). This could possibly create a condition where the next round rising between them might be slowed by having to "wiggle/snake" side-to-side between them as it passed them, and it might slow the round's rise just enough to create a feeding/timing problem. I was told they replaced any mag which might have that issue ... and of course, one of the other guys and myself each had some early CS45 mags which occasionally exhibited such issues and which the company replaced. That was many years ago.
Something else it might be prudent to remember is that reduced size .45's ...of virtually any make/model ... can have reduced weight slides, shorter slide travel and increased slide velocities. Heavier springs can mitigate this to some degree. However, the same short and wide profile .45 bullets are still having to be fed into the barrel chamber, and the same length rounds are having to be released at an optimum point to allow proper feeding & chambering.
While all this is happening, the smaller .45's seem to be less tolerant of the shooter (grip support & wrist lock) and ammunition (nose cavity, OAL and power levels) influences than their larger cousins. I've seen some folks "limp wrist" a CS45 virtually "on command", and I've unintentionally experienced it myself when my attention was distracted from my grip during some shooting drill and course of fire.
Bottom line? The diminutive .45's ask more of the shooter and ammunition than the larger models.
I've found my 4513TSW's (both my original model and a newer production issued model) to be less sensitive to such issues ... in my hands ... than my CS45.
Just my observations and thoughts ...