How do I choose a Mariadb version to install, and what is the difference between mariadb.com and .org? I have not worked on databases before but I am needing to research information about databases for work  

I will be using Mariadb  

What should I look for when choosing which version to download? It looks like the latest version is 10.4.12-GA, but it is only available for Ubuntu 18.04 (only relevant Ubuntu option in the drop down menu here). I will be using Ubuntu linux in the database server computer, and it looks like the latest Ubuntu release is 20.04. Should I use the latest Ubuntu and latest Mariadb, or would it be better to stick with Ubuntu 18.04 and the latest mariadb? Also, this page says that Mariadb 10.1 is included by default in Ubuntu 18.04. is that the recommended version?  

One issue that was brought up during our discussion was the interoperability between Mariadb and MySQL. It looks like after version 5.5 the version numbering between the two seems to have diverged, with MySQL at 8.x and Mariadb at 10.x, with the 10.x version being compatible with the 8.0 version. Is this something I should be concerned about? Our database server computer will only have Mariadb and since we are not upgrading from an existing database nor do we intend to change to some other database in the future, I don't think I need to worry about compatibility with MySQL, but I just wanted some opinions on this.  

Lastly, a quick google search brings up mariadb.com and mariadb.org. For example, searching "mariadb download" in google gives me https://mariadb.org/download/ and https://mariadb.com/downloads/ as the top search results. Are both of them the same thing? Which one should I be using?
On downloads, I'd go with the MariaDB.org repository management tool. There is only one 20.04 focal release for the 10.5 Beta branch at the moment (so not recommended yet for production use). The reason is that the releases include what distro builders where available at the time of release so as time goes on there will be a focal repository for every major release.

Until that happens, focal includes a 10.3.22 package version which is a good starting point.

On a normal fresh install I'd pick the latest GA stable (10.4) however since there isn't easy packages for focal yet, stick with the 10.3.22 distro package.

MariaDB.com releases are tarball only installs making upgrading harder.

On MySQL vs MariaDB, there is a large (and dry reading) compatibility page describing differences.

As its a green fields install there isn't a lot to worry about with compatibility. The main thing to look at is if MySQL/MariaDB has the features you need.