No, the main difference is that MySQL bundles the code needed to interact with the old db version in the newer server binaries (effectively by not changing the on-disk binary format!) while pg_upgrade requires you to have both old and new installs living side-by-side to reuse logic/code from old binaries. It is a more bulletproof method and less susceptible to bugs and (upstream) developer errors, but is (or at least can be) harder for the sysadmin+dbadmin.

(For example, ports under FreeBSD doesn’t let you install multiple Postgres versions as they are marked as conflicting packages so installing one necessarily uninstalls the other. The saving grace here is that most (virtually all) FreeBSD installations have root on ZFS and you can employ ZFS snapshots (via the hidden .zfs folder) to access the old binaries after upgrading to the new postgres version, but not many people know this trick!)