What I think made screens feel different was as a grouping mechanism, usually driven by a single application (though in more recent versions of AmigaOS you could open "public screens") that would manage the layout for that screen. You can do that with virtual desktops, but it takes some effort to simulate the behaviour.
I'm slowly iterating on something like that for my wm. I now snapshot the (by default tiling) layout and restore it, letting me "open" and "close" screens/virtual desktops, and re-open the applications on them, so instead of opening a single application that opens a screen, I will open a "project" and it will open a desktop and multiple applications on it whose windows will snap into place. I'm not happy with it yet, but it feels somewhat closer to me to how it felt to use Amiga screens.
Some systems like Xsgi went further with having several visuals used for predefined purposes in their modified Motif versions
- 3D apps (games) render at a resolution less than the desktop for performance reasons (even in fullscreen mode to avoid switching the video signal)
- Similarly, streaming sticks/TVs render the UI at 720-1080p and overlay on hardware decoded 4K video (very common in anything that's not a console, Apple TV, or NVIDIA Shield)
- Handling non-high DPI apps on a high-DPI desktop, or handling systems with mixed DPI displays
- Combining HDR and SDR content on the same desktop. Same with deep-color apps.
- UI effects like the OS X genie effect, app thumbnails