I use the (GUI) archive managers of Linux Mint, LMDE and Linux Lite.

I 'tar' files with them and I do not see much difference between them.

But I'd like to know if it would be possible to, for example, create an archive (tar.gz) on Linux Mint and then extract the files in that archive
on Linux Lite.

Whether such an intention makes logical sense is another question, just like to know if there would be technical problems with doing that.

This is an odd question - people share tar.gz files all the time, across a myriad of different OSes, and have done for decades.

A tar.gz is simply a tar file with gzip compression applied. Both of these things are standards, thus if you create a file with standards-compliant software, all other standards-compliant software will be able to read that file. Any failure would be a bug in one of the pieces of software involved.

I'm sure there's an XKCD toon that covers archives. (If not, there ought to be. )

In a previous life, I routinely had to move patch files received from a major software vendor's Tru64-based application that were, in theory, in a tar.gz format but couldn't be read on the Tru64 system until: 1.) I moved the archive from Tru64 to Linux, 2.) unpack and re-tar/gzip, and then 3.) move them back onto the Tru64 box. Then the native tar could read them. Fluky problem to say the least. (Only one reason I despised working with that software vendor.)

The archive manager is just a GUI front end to the GNU tar utility which should be the same on just about any linux distribution. As posted a tar archive should be OS agnostic i.e. any OS i.e. Unix, linux, MacOS, Windows, VMS etc.

.tar.gz is so standard that you're never going to have a problem.