Installing "xyz firmware" vs Rooting on "xyz firmware". What's the difference between rooting on a particular firmware and installing a particular firmware?

Does that mean to root on "xyz" you must have installed "xyz" on your device?
As it says:


"root on XYZ" means XYZ is a pre-condition for this rooting instructions (so yes, it must already be on the device)
"install XYZ" means, well, to install XYZ (whether it already was on the device or not).