Think of the Shorty 45 as the limited edition, or "LX" model of the 4513. It comes with all the custom bells and whistles of a target/competition gun, on a model 4513. In fact, the Shorty 45 MKII IS a model 4513.
The Shorty 45 has a Performance Center airguaged match barrel and Briley barrel bushing. The Briley bushing fits tightly to the muzzle of the barrel, increasing accuracy. The fit and finish of the PC Shorty 45 exceeds that of the standard production 4513's as well. On my example there is not a tool mark to be found, and every seem matches up perfectly. Tight fit too. No shake or slip to be found. Differently cut slide too, with lightening slide cuts down either side. The bottom sides of the slide is bevelled as well.
Add the Performance Center trigger and a lack of MIM parts, and you have a superb compact carry 45, that outshoots my Colt Gold Cup, and Kimber Stainless Target II, and cost much less than those pistols.
There are two versions of the "standard" 4513TSW pistol. Although calling the 4513TSW "standard" belies what you get with this particular pistol. While lacking the match barrel and Briley bushing of the Shorty 45, the 4513TSW is no slouch in the accuracy department. When shooting both guns, the groups never vary more than one inch with either.
I've owned both 4513TSW versions. The first version had no idiotic rail on the dust cover (A big plus for me. Why hang a rail on a compact CCW pistol???), and had a chopped, or shortened grip frame. The mags for this version were 6-round. Still, a 7-round capacity is nothing to sneeze at. In fact, is that not the capacity of the vaunted 1911 that others go on and on about? But I digress. Ambi safety was standard on both versions, as were the OEM Delrin grips.
Hogue does not make a rubber grip for the chopped grip frame 4513. Although some enterprising 4513 owners here have cut up Hogue grips designed for the second 4513TSW version, and adapted them to the abbreviated grip frame 4513 with good results.
The second 4513TSW has the same dimensions as the Shorty 45. It has the rail mounted to the dustcover. If you prefer it is a simple affair to remove it. Drill out the rivets, and drop it. That easy. The second 4513TSW has a full grip frame and a 7-round mag, giving you the 8-round capacity of the Shorty 45. Both the Shorty 45, the late version 4513TSW and the 45 Recon as well as the 4556, and 4516 all share the same mags.
I purchased all the versions of these S&W 45's you inquired about, and have no complaints with any of them. Reliable, accurate, light weight, and easily concealeable. Best compact TDA 45's on the market, IMO. Best gun money I ever spent too.
I have staked my life carrying all three of these, and that is about as good an endorsement as you can give any product. Hope this helps! Regards 18DAI.