Windows 1/2, 3 and 3.1 do have different colour systems, afaik.
Windows 2.x uses a virtual tru-color system and works perfectly if it can use 256 colours.
All higher colours are created through using dot patterns (dithering).
On 12-14" monitors it looked really nice, almost indistinguishable from real tru-color.
(Windows 3.0 real-mode kernal works similar if it is forced to use Windows 2 drivers.)
Years later, Windows 3.0 switched to the palette based system as we know it, which technically was a little step back.
But image quality increased on the larger monitors of its time, since dithering wasn't used anymore. For normal operation, I mean.
Images/applications using a high colour still forced Windows into dithering, of course.
Almost all image manipulation programs like Photoshop, IrfanView or Graphics Workshop were affected.
Except the popular WinGIF, maybe, which was weird. But it was primarily made for GIF files, anyway, which have a 256c limit.
In Windows 3.10, the dithering algorithm and the colour management slightly changed.
In Windows 3.1x, 16 colours are static colours or system colours.
If the graphics drivers support a higher colour depth, say 256c, that number is increased to 20.
Thus, 236 colours can be used freely by applications or image viewers.
If that limit is exceeded, the desktop shows those trippy colours or background applications become monochrome.
That's one reason why programs like Autodesk Animation Player for Windows (AAWIN)
have a menu option to use/not use full palette, I assume.
What's neat about 256c is, that it is palette based.
It's possible to simulate movement and animation by applying a technique known as "palette cycling".
Games like Descent used it (the fading animation at the start), and famous graphics programs like Deluxe Paint.
Or fractal generators, like FractInt for Windows.
Games/applications using WinG often say that they want 256c graphics modes.
This happens both with 16c and higher-than 256c colour depths.
I've noticed that when testing old emulators on Windows/Win32s.
Last but not least, the Windows help has a bug if run beyond 256c.
The hyper links are green in 16c/256c colour-depth, but become black beyond 256 colours.
Edit: It's also possible to use colour-cycling in Standard VGA (mode 12h).
There was an experimental driver in Windows 3.0 MME (palletized).
Unfortunately, not all applications will work with it because they don't expect a 16c driver to be that flexible.
Edit: I'm speaking under correction, but I think that past 256 colours, the palette system is nolonger being used.
I'm not saying it's not possible, but the Windows graphics drivers seem use a direct addressing method for 256+ colour depths.
Edit: Little edit.
Edit: Yes, my experience is similar, most Windows 3.1 applications will still work beyond 256c.
I haven't noticed any major compatibility issues yet.
However, some applications run smoother or look more natural if being run "natively" in 256c.
Certain animation effects are also exclusive to it.
That's why later Windows version have an compatibility option for 640x480 and 256c in compatibility tab, I suppose.
Interestingly, some early Windows 95 era games may have a few minor issues with 256+ colours also. Or impose a 256c colour limit, rather.
I vaguely remember that one of the Sega PC titles,- I think it was Sonic CD-,
had video files stored in hi-color/tru-color, but the game engine always applied dithering.
This was so weird, because playing the video files on Windows 98/XP (in hi-/tru-color) in Media Player didn't cause any dithering.
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