Can I use the macOS from a late 2012 Mac mini on a 2011 Mac mini server?

Your Mac mini 2012 supports OS X 10.8.1 up to the current macOS (10.15.1 at the time of writing). The Mac mini 2011 officially supports OS X 10.7 up to macOS 10.13.6 (High Sierra).

After upgrading your Mac mini 2012 to 10.14 (Mojave) and further trying to upgrade to 10.15 (Catalina), the Mac mini 2011 won't boot with this system disk.

The Catalina installer can be patched to run on some officially unsupported Macs and install the latest system.

The Mac mini 2011 (Macmini5,2) is on this list of (patch-)compatible Macs (with the restriction: ...systems with AMD Radeon HD 6xxx series GPUs will be almost unusable when running Catalina.). The Mac mini 2011 Server (Macmini5,3) - also on the list - doesn't contain an AMD Radeon GPU.

I don't recommend to use such patch.