Before posting I wanted to confirm what I read in the past about this cartridge. It was developed as a straight wall deer cartridge for states where bottle neck cartridges are prohibited. IIRC the main complaint was the didn't use the .38 (.357) caliber bullet which would have given it more versatility.
https://en.wikipedia.org/wiki/.350_Legend
The WIKI page is often cited since it lists the 350 Legend as using .357"
The initial spec sheet proposed to SAAMI had the chamber neck diameter too tight for .357" bullets but was quickly changed to possibly allow for .357" bullets at least on paper. When people measure the bullets on factory ammo they find them to be .355". The push for winchester to say .357" comes from them wanting more sales. Sort of like 357 sig is a 9mm and should be called 355/9mm sig, but even less people would buy it. They're playing a stupid game that since there is overlap between .357 magnum tolerances and 350 legend tolerances that they are the same thing so that users in states that have a minimum caliber of .357" would be allowed to use them. Don't get me wrong, I feel the .002" difference is so minor that you'd never be able to tell a difference on any shot game in the field. Winchester knew that going in and could of gone with .357" sized bullets and bores. So why lie about it unless there is some financial reason like sales and cutting out huge sections of your potential customer base?
The 350L calls for a .357" bullet with a tolerance of -.003" compared to the SAAMI specs for 357mag Lead bullets .359"with a tolerance of -.003, or jacketed .358" with a tolerance of -.003". Similar tolerance applies for barrels where the minimum barrel bore diameter of the 357 mag is .355" with a tolerance of + .004" and the 350l is .355" with a tolerance of + .002". The freebore diameters are: 350L .357" +.002"; and 357Mag .357 mag .357" +.004". Some guns out there like the Rugers, have a chamber who's tolerances are on the larger side and will easily chamber .357" diameter bullets. Others will not as it is possible by the specs to have a .357" bullet and .357" freebore which is tighter than normal +.0005" over bullet diameter match chamber freebore. Even winchester who will say that their bullets in their loaded ammo are .357" sells the same bullets for reloading as .355".
https://www.midwayusa.com/s?searchTerm=350+legend+bulletsThe case is also unique. The 357AR is basically a rimless 357Max run at 55K psi made from 223/5.56 cases with a little added body taper to get it to feed better usually with a .382"-.385" base diameter of the chamber to the .392" of the 350 legend. I agree that the extra case taper would only help it feed better, but it's not really needed as they feed fine at .382". There are also guys that make 5.45x39 cases with a similar base dia of the legend out of 223 cases. so 223/5.56 cases can be used but you'd have to be willing to accept more case failures and a shorter reloading life. Starline has 223 basic brass which works great for 357AR and I've seen where guys made 350L with it early on. Usually I'll get close to a dozen loads out of a 357AR RP/WIN case or a few less out of the starline if you keep the loads reasonable.
The case length of 1.650" v/s 357max/357AR at 1.600" is what gets me. They're both meant to be fired out of an ar15 so you have the COL limits of the magazine for both which means that extra case length on the legend is only covering up the bullet .050" more, so why do it? There were very few 9mm bullets that could handle 350L speeds when it came out but there were some .357"-.358" bullets that could handle the same speeds and be in the 158gr-200gr sweet spot for both cartridges. With the longer case length prevented some bullets from being used because the casemouth was now into the bullet ogive which gives you a smaller case mouth diameter which will cause issues on a case that headspaces on a small .010"ish step in the chamber. Headspacing on the case mouth is the main reason I feel they went with 9mm bore over .357. If the casemouth dia is too small the crimped area can slip into the freebore which will prevent the casemouth from opening up when fired. Most of the 357/358 bullets have a cannelure and reloaders that don't understand how a straight walled cartridge headspaces can't help themselves from roll crimping good n tight into the cannelure which can cause excessive headspace. Since winchester went to the point of making a new case they should of made a new belted case. Headspace would no longer be an issue and idiots could rollcrimp to their hearts content.
Inclued is a pic of basically my last point on headspacing. The case separations were caused by a bad chamber and winchesters own ammo that didn't meet it's own specs for minimum case mouth diameter. The cases were slipping into the improperly cut freebore and were unable to expand as described above. you can see the steps on the casemouths where they slipped into the freebore, and the miscut freebore where the rougher reamer was pushed in too far and reduced the casemouth/freebore step in the chamber which allowed it.