Lets run the list of the biggies:
British Flanged -.577, 303 Brit, .455 Webly, all of the British Express rifles, .44 Bulldog/Russ/spec/mag, 30.30 (all of the Winchester lever rounds), 30.40 Krag, 45-70, 220 Swift....
British (Holland & Holland) Belted cases - All of the Holland & Holland cases, Weatherby cases and our belted Mags.
Mauser - All of the old 11.5s and 11.7s and other, the variations of the 8MM (7.95, 7.65, 8X57, 7MM, more), 30.03, 30.06, 25.06, .243, .45ACP, and on and on.
9MM Lugar/Parabellum - .222 Rem, .223 Rem mag, .223/5.56, .221 Rem, .17 Rem, .300 BlackOut. But hold on, it is just a smaller version of the Mauser head, scale it down.
.32 S&W/.38 S&W family (just size versions of the British Flanged)
And .38 Long Colt/S&W Special (again the British Flanged) .22Jet
About the only real new head of late (in general uses) is the 10MM/.40S&W and I see it only as a size change from a conventional existing casing (Mauser again).
No they are not exact (anymore) and will not all exchange. But they have common case and more importantly head dimension back grounds. It comes down to re-inventing the wheel or in this case (pun intended) shell casing. If an existing case/head will work, use it.
Three major types: British Flanged (rimmed), Belted, and rimless. That just about covers them, some a little larger/smaller/thicker/thinner.
These are my explanations and may or may not be based in facts. Yes, I know I missed the great XXX casing and many others, but you get the idea.