This requires some clarification for future readers, and I happened to be in the neighborhood:
IF YOU ARE TALKING ABOUT DISTRO VERSIONS (Ubuntu, Kubuntu, Xubuntu, Ubuntu Studio):
Yes they do. The same drivers will work on anything, even Bodhi Moksha is based on Ubuntu, as are many other distros with weird names. Just make sure you are using the same VERSION NUMBER. (read about that next)
IF YOU ARE TALKING ABOUT VERSION NUMBERS:
No they do not. For example. NVIDIA dropped support for GT Series that uses 390 drivers in >= 22.04. There won't be any, ever. This is because the CUDA and other technology is a industry asset that isnt to be shared with open source community. Once upon a time NVIDIA was considered the standard for "continued" linux support across all their cards that were still largely in use, now its following suite with AMD/ATI and only supporting so many years back or not at all in some cases. (you can see if your nvidia card is supported by simply typing nvidia-detector on a command line in a terminal).
WHY IT HAPPENS
This happens largely because nobody wants to update the kernel code or there is just no programmers to do it, or the workload is too great, or they just don't want to do it anymore. On the other end, whenever something updates the kernel in an incompatible way, the drivers need changed. This is unlike Windows where drivers are not as strictly incorporated into the kernel or requiring specific kernel features.
VS
For this reason Windows drivers are far more usable. Sometimes you can even use drivers for a completely different platform. Driver support is one thing that Windows has always had over Linux, hate to say it. I doubt this will ever change unless someone solves the "kernel-sock-blocking" problem. But then again, we might just need one person to think in a completely different direction and show us how simple it is to fix :3 (seen people do this a few times through the decades).
PLAN AHEAD
So, before installing any OS be sure to verify your card is compatible with THAT operating systems. Nowadays, even the not-so-smart search engines can give you a ballpark on that, and go from there with whatever links it throws at you.