With the update manager constantly updating software, what does it really mean to upgrade Ubuntu?

Solution 1:

Unless you've added extra repositories, Update Manager will only offer to install stable release updates, which are updates that fix either high-impact bugs, or security vulnerabilities. Some rare exceptions notwithstanding, they don't provide new upstream versions of software that constitutes Ubuntu.

A distribution upgrade, on the other hand, does: it takes you from one Ubuntu stable release to the next, thus most packages you have installed will typically be updated to new upstream versions.

Solution 2:

Everyday update -> security fixes, minor improvements - (all software you use stays at the same version, which is a bit older than current, but much more stable)

Distribution upgrade -> new features, new pieces of software, major changes - (every part of your ubuntu gets upgraded to new version, that was developed since last ubuntu release)