clean install: you make a backup, nuke the computer, install a fresh upgraded copy of the distro you want from a live usb, copy your data again to the computer.
upgrade: you wait 'till the distro' developers release an upgrade you can directly install from your soon to be old distro, you use a command like sudo do-release-upgrade
and why do you upgrade like that?
This is my plan A. I'll only go to plan B if something goes wrong — which has happened to me a couple times. I tried to upgrade Ubuntu (LTS, I forget which version) years ago, but it failed hard. I still don't know why. It wasn't something I could figure out in half an hour, and it wasn't worth investing more time than that.
Come to think of it, it's possible all my upgrade woes came down to Nvidia drivers. It was a common problem on Suse (TW), to the point where I pinned my kernel version to avoid the frequent headaches. I'll try a rolling distro again when I switch to AMD, maybe.