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?
Depends on the distro.
On my personal laptop with openSUSE, I have plenty confidence doing all kinds of upgrades and sidegrades (between Leap and Tumbleweed).
The package manager detects conflicts and makes me decide what to do with them. I've never seen the software or distro dependency definitions fuck up, it was always me making a wrong decision.
Well, and if I do make a wrong decision or anything else should go wrong during the upgrade, I can roll back to the BTRFS snapshot before.
On my work laptop, the best I can get is Kubuntu. Apt is much more fickle, since it doesn't have as clear of a concept of what constitutes a conflict, but also what a correct system should look like.
The whole packages feel much more fickle, too, because they've got all these custom patches, so you really don't want to accidentally mix different versions of packages, like might happen in an incomplete upgrade.
And of course, you get one chance at upgrading. If anything goes sideways, you better have your Live USB ready right away.
So, that's why I would prefer to install fresh right away. Of course, my workplace doesn't actually allow me to do that either. They really like to keep me on edge.