Why are their bullets seemingly incompatable? As far as I know, the desert eagle is the only semiauto pistol to use revolver rounds - but it’s a bit of an oddball, being gas operated. And I’ve never heard of a revolver using semiauto rounds.
Is there some fundamental reasons that one’s ammunition won’t work in the other’s general design?
The cartridges are usually different in self loading pistols versus revolvers but the bullets are a different matter. There are plenty of exceptions in both dirctions but for the most part self loaders use rimless cases while revolvers use rimmed cases.
Most modern revolvers use cartridges with a rimmed case. This allows a star ejector to extract the empty cases. The cartridge also headspaces on the rim. That means the rim limits how deep the cartidge goes into the chamber. This allows shorter .38 special rounds to be fired in a revolver with longer .357 magnum chambers.
Rimless cases feed better through a magazine so they are generally preferred for a self loader. With no rim the cartridge must heaspace on the case mouth.
You noted the exception of the Desert Eagle using rimmed cases in certain calibers. Some specialized self loading target pistols are chambered for .38 or .32 full wadcutter cartridges.
In WWI there were not enough of the new Colt 1911 pistol available so Colt and Smith & Wesson chambered double action revolvers for .45 ACP. The rimless cartidge could not be extracted so they were used with half moon and full moon clips, a stamped bit of sheet metal that snaps into the extractor groove of the cartidge. This allowed three or six cartridges to be loaded at a time and to be extracted just like rimmed cartridges. There is also a .45 auto rim cartdige which has an extra thick rim to take the palce of the moon clips.
The OP is right that in general autoloaders and revolvers have their separate families of cartridges, without a ton of crossover. Here are some exceptions:
Cases 1 and 2 make use of moon clips to extract the rimless cartridges. Case 4 uses a spring-loaded star extractor which slips into the groove between rim and case. Case 3 is pretty obscure and I have no clue.
Cases 5 and 8 are target weapons with small magazines. I suppose that the revolver cartridges were/are considered inherently more accurate than rimless varieties? But there are plenty of super accurate pistols these days in regular old rimless chamberings, so maybe thinking has changed.
Case 6 has already been discussed. 7, 9, and 10 are similar for our purposes (although they don’t operate on the same principles) - they are large, expensive pistols designed for hunting and impressing cinema audiences.
This cartridge is an interesting case. It was developed from a revolver cartridge (44 Magnum), but first chambered in an autoloader (the Desert Eagle). It is neither rimmed nor rimless, but instead uses a rebated rim (i.e., it kept the the 44 Mag rim but has a fatter body, so the rim is actually smaller than the case). Actually I don’t know how these revolvers extract since they aren’t swing-outs, so they wouldn’t use moon clips, but I don’t know what the rod would push on to get the brass out of loading gate…
This is a new one on me. Are you thinking of the Model 52? If so, I assure you that it uses rimless cartridges. If not, please fill me in as I’m a collector. Thanks.
ps…I’m always looking for sources for the disassembly tool for Model 52s…
OOOOPPPS!
Having already committed myself in writing I decided to double check and Boris B is correct. The S&W Model 52 does use rimmed cartridges. Never mind.
Hey, I was about to double-check myself. I think the thing about the Model 52 (and the imported .32-cal. target pistols), as Padeye mentioned, is that they only work with wadcutters. I suppose this is because round-nose bullet would be too long? So I guess it’s correct to say that S&W 52s don’t work with ordinary revolver ammunition, since I don’t think wadcutters have ever been the best-selling 38 Special load.
As stated, revolvers tend to use rimmed cases. I can think of two reasons why rimmed cases are not good for semi-suto applications: First, the magazine would need to be loaded carefully so that each round is slightly more foreward of the subsequent round. This is because you don’t want it to get snagged on the rim below. The other reason is that rimmed cases are larger in back than along the body. This would require a curved magazine that would be difficult to fit into the stock/handgrip of a pistol.
How on Earth could everyone have forgotten the lowly .22 rimfire? 
You can get guns that fire it in both revolver and semi-auto form quite well (Ruger .22 pistols are very reliable semi-auto pistols, even with a rimmed case shell).
Holy peashooters, Anthracite! And I have one of those! The magazine is designed so that the rims will not overlap when loading.
Well now, feeding problems with rimmed cartridges affect nearly all weapons fed by vertical box magazines, not just the semi-automatic ones. This is why the .30-06 cartridge was designed as a rimless; likewise the 8mm Mauser and a bunch I haven’t thought of. The British are, on the one hand, criticized for using the rimmed .303 cartridge in box-fed weapons (e.g. the Lee-Enfield, the Bren), and admired on the other hand for making them work so well in spite of this.
So the distinction we’ve made on this page between rimmed and rimless handgun cartridges has an analogy in rifles: rimmed cartridges are for lever-action repeaters fed by tubular magazines, and for break-action non-repeaters. Rimless cartridges are for bolt-actions and semi-automatics fed by box magazines. As before, exceptions abound; it seems like whenever John Browning heard a rule stated as “such-and-such ammo won’t work in such-and-such weapon” he went out and designed a gun to prove the rule wrong.
Anthracite made a good point about rimfire .22s. These are rimmed cartidges, and are usable in both pistols and rifles of every know type of action/magazine: single shot, semi-auto, full auto, pump, bolt action, lever action, revolver, tubular magazine, rotary magazine, straight magazine,and curved magazine.
This fact would seem to give the lie to claims that rimmed ammo cannot be used in autoloading weapons. I agree that rimless ammo presents some problems with extraction in certain types of actions (e.g. revolvers), but these can be overcome by mechanical design…e.g. extractor springs ath grasp the groove of rimless cartridges.
It’s a matter of practicality that rimmed and rimless cartridges are used in different systems. The lowly .22 proves this.