ACP vs AR vs LC
Randy - As pointed out above, the AR brass is made to use 1917-pattern revos without the full, half or third-moon clips. At the beginning of WWI the 1911 manufacturers could not produce enough of the slab-sided shell-shucker, so S&W and another manufacturer adapted their 44.45 frame revolvers to use the ACP in the ingenious invention, the half-moon clip. This has evolved to the present 25/625. The 45AR rim is very thick (it uses a unique shell-holder/shell-plate) to take up the space vacated by the missing clip. It headspaces on the rim like a conventional rimmed round, therefore you can use a roll crimp on it. I consider it a better choice than ACP brass for making shotshells for that reason. HKS makes speedloaders for it, so you aren't stuck single loading it. For years, Remington had a monopoly on the brass and the price reflected that. Now Midway carries Starline and it's affordable. The new shell-plate for a Dillon is a different story.
The reason you can't interchange LC and ACP cylinders on an existing gun is that the cylinder lug at the bottom rear of the cylinder window is DIFFERENT between the two. Again this is because of the thick rim/added clip. S&W has yet to resolve this glitch and allow interchangeable cylinders. TK Custom can machine your LC cylinder to accept ACP in moons and still headspace LC on the outer half of the cylinder face, BUT just like the 'omnivorous' 45ACP/45LC revo made by a competitor firearms company, you then have the 45 ACP bullet leaving the ACP case and rattling down the remainder of the LC chamber, having to either obturate to seal itself to the chamber or be gas-cut all the way to slamming into the cylinder throat and then negotiate the forcing cone. I don't see how that results in any kind of accuracy. Also that configuration cannot digest 45AR.
Until S&W makes it easier to swap cylinders, that's the terrain.
If you want to swap cylinders, that scenario is for the time being restricted to the SA revolver universe, which is not a bad way to go if your revolver use is sporting and not duty/defense.
By the way TK (they made the clips that shipped with your 625) will do that milling and supply clips for almost any rimmed-case revolver configuration. I haven't had it done on my 29 nor 66 nor 686 nor 27 because A, I have a wheelbarrow full of speedloaders, and B, it's about $300 for the work and a batch of clips. I hope this clears up the ACP/AR/LC fog for you.