Traditional desktop means regular desktop environment. The other one starts in big screen mode, like the handheld devices so you do not have a desktop. That’s the only difference between the two. Both comes with Steam pre-installed.
Because they use Steam’s Big Picture mode to give it a handheld function. In handheld gaming devices you do not have a desktop, but it launches straight into some sort of game launcher. In this case it is Steam’s Big Picture mode.
Again, they both come with Steam pre-installed.
Edit: to make my explanation even clearer:
Steam Gaming Mode = Steam’s Big Picture mode where you do not need a keyboard and mouse but can navigate using only a game controller. Which is pretty much necessary for handheld devices like Rog Ally etc.
Traditional Desktop Experience = Your run of the mill desktop, where you will have to have a keyboard and mouse to navigate.
Bazzite is a gaming-focused distro. It comes with Steam, Proton tricks, Mangohud, Gamescope and many other things preinstalled so it is ready for gaming out of the box, regardless of whichever version you choose. I hope this clears things.
Second edit: Here’s a quote from the official Bazzite website:
“Bazzite is designed for Linux newcomers and enthusiasts alike with Steam pre-installed, HDR & VRR support, improved CPU schedulers for responsive gameplay, and numerous community-developed tools and tweaks to streamline your gaming and streaming experience.”
Although, I am not a gamer I was looking into Bazzite because it offers direct support of ASUS laptops by including packages asusctl and asusctl-rog-gui and also including the asus-armoury driver.
However, when switching to DX both packages are gone. So it seems that either Bluefin or Aurora are better suited. Depends upon my decision to decide for Gnome or Plasma.
I anyway have to find out how to create a custom image. The benefit would be that then the two asusctl package would not be layered.
But in order to get the asus-armoury driver running I would need a customized kernel which looks like to much effort (at least currently) as I am currently testing things to make sure I can be productive with Aurora as I was before.