As is the case with a lot of things when they're in their early stages, early semiautomatic pistols had a lot of variation as different methods were tried out. Over the years, systems fell by the wayside, either due to obsolescence, political expedience, or market availability.

The big defining feature you're looking at here is the pistol slide. The slide, which first made an appearance on Browning's FN Model 1900, takes on the duties of a bolt (housing the bolt face, firing pin, and extractor) while sitting largely outside the frame of the gun and extending forward. This offers several benefits. For locked-breech pistols (most everything stronger than .380), this provides a surface for the locking mechanism to attach to, and for blowback designs, it allows for much of the reciprocating mass to be put forward of the bolt to keep the design compact. In terms of ergonomics, it also provides a larger surface for the user to actuate the mechanism (as opposed to the "wings" on the bolt of a C96 or Nambu), as well as providing a lot of surface for things like a slide release or safety to be added.

Additionally, all of these guns have the magazines in the grip - something intuitive now, but not necessarily the norm for all early handguns. The Mauser C96 is perhaps the most well-known example of such a pistol.

So what made these designs so much more popular? Simplicity played a large part. Browning designs (most early FN pistols and the 1911 among them) were much simpler guns to manufacture and operate than contemporaries like the Mauser C96 or Luger. The C96 in particular is practically clockwork on the inside, making maintenance and replacing parts difficult. Meanwhile, the simpler designs offered by Browning-style pistols are comparatively easy to both manufacture and disassemble for maintenance.

Additionally, the commercial availability of the designs can't be discounted. Just as the Mauser rifle became prevalent all over the world largely thanks to the commercial efforts of FN Herstal, the Browning pistols designs benefited from FN's commercial success as well. Especially once FN had been taken over by DWM and had to focus its efforts on areas other than Mauser rifles, the pistol market became a huge part of FN's focus. FN pistols (and by consequence, the Browning design) ended up all over the world, becoming popular in their own right and influencing local development where they went. The Tokarev pistol, for example, copied much of the Browning design, and mechanically is largely a 1911 in 7.62 Tokarev. Adding to that, there were numerous Spanish manufacturers that became notorious for copying (and often improving upon) commercially successful designs, especially those of Browning.

And then there's the political expediency of these designs. Browning-style pistols ended up being the primary style of semiautomatic handguns used by the victors in WW2. The Luger, while emblematic of Germany, was already starting to be replaced by the cheaper Walther P38 by mid-war, and the disarmament of the postwar period and ensuing Cold War accelerated this trend by encouraging East and West Germany to move towards standardizing with their respective blocs. The Nambu in Japan would stick around through the postwar period, but it too was replaced by conventional Browning-derived designs that would be both mechanically superior and more powerful (the 8mm Nambu pistol cartridge was notoriously anemic). On the Soviet side of things, pressures to standardize on Soviet equipment meant that their conventional designs (Tokarev and Makarov pistols) would proliferate through their allies. Where exceptions did exist as in Czechoslovakia, they still opted for slide-based designs.