Can I change the Linux distribution without formatting or losing my data? [duplicate]

TL;DR: Take a backup first, you'll need it.

While Zorin OS based on Ubuntu, they are completely different operating system, employed by different manufacture. If you want to switch between them, I strongly urging you to perform a backup first, it's better to be safe than sorry.

This is also mentioned on their forum, when a user asked how to migrate to Zorin without losing data, everybody seems to advise the said user to take a backup first.

If you somehow have a dedicated partition for /home folder, you can simply format your system partition and then install Zorin onto that partition. It should work— but you should have take a backup before, I wouldn't risk it.