It would seem that no other technology has as much incompatibility between the Americas and Europe than slide projectors. Europe has several standards of theirs and North America has several standards of its own.
I notice even that Kodak Carousel projectors on the European market look completely different than American Carousels, and I'm guessing that a Kodak Carousel tray from Europe won't fit an American Carousel (and vice-versa).
I'm only knowledgeable in the American slide projector scene, so I don't know what works with what in Europe. The one exception on our side of the Atlantic was that a few camera stores did offer Leica Pradovit models and sold the Leica straight trays to fit them.
For those in Europe who might wonder what trays were being used over here:
Circa 1954-1963:
Two systems dominated.
The Airequipt Magazine was a straight tray made of metal (I think mostly Al, judging by the weight, for which each slide was placed into a metal frame, and 36 such framed slides slid into a metal tray. The Airequipt Automatic Changer started as an accessory that could be fit to many makes of projector, though Airequipt and others would later design projectors around them.
The common competitor was the "TDC" tray, a simple plastic straight tray that contained the slides individually in (usually) 30, 36 or 40 spaces, with no friction, meaning a tray cover held the slides in the tray, and one had to remove the cover carefully and place the tray into the projector, without turning the open end below the horizon, lest they all spill out. The advantages were that these trays were less expensive than Airequipt Magazines, and easier to load and unload. So many manufacturers adopted this design, that they came to be called "Universal" trays. Another quirk was that whilst most of these projectors moved the slides horizontally, a few (e.g. the Ansco Regent) worked vertically, thus one set of slides loaded into a TDC tray might produce sideways images when used with another projector.
In this era, there were several other straight plastic trays that looked a lot like the TDC, but were not compatible, but few projectors used these.
Early 1960's onward:
Kodak introduced the Carousel tray system, with an 80-slide tray atop the projector, like a Carousel, and kept that business pretty much to themselves. It was very successful, and Kodak would introduce another series of projectors that could use either 80-slide or new 140-slide Carousel trays (the first-generation Carousels, as the 550, were still limited to 80-slide trays, however).
Sawyer's answered with the Rototray, a 100-slide round tray that sits in the projector upright, as a Ferris wheel. In this design, thin metal clips hold the slides in place by friction, so no collar is needed to hold the slides. Since the design of the tray is similar to a TDC tray, extended to 100 slides, then bent to form a torus and joined at the ends to itself, Rotomatics (the Sawyer's projectors designed to use the Rotoray) were also able to project slides in TDC straight trays (unlike the Carousel projectors, which were not compatible with any tray, save the Carousel). Unlike Kodak, Sawyer's licensed the design to several other slide projector manufacturers, so it is almost as common as the Carousel.
Soon afterwards, several companies introduced other tray designs of their own, thinking they could make more money by limiting customers to purchasing only their own trays, but this left a lot a projectors that needed hard-to-find trays, and those competitors faded away quickly.