As Spinlock alluded, mariadb is a fork of mysql to try and prevent licensing issues once mysql's parent company was bought by Oracle. When the fork happened, most mysql developers moved to mariadb. A lot of companies and distros have switched to mariadb, including Slackware.
The developers for mariadb have made it a point to maintain compatibility with mysql, so if something worked on mysql, it is very likely it will work with mariadb. There's likely no reason for you to install mysql on Slackware and I'm not sure of any projects with SlackBuilds for you to easily build mysql (although, you might be able just change the mariadb SlackBuild to do this).
Slackware switched to mariadb during the development of 14.1 and has used it since. Here's the changelog entry of that switch with just the mariadb stuff:
Code:
Sat Mar 23 22:49:52 UTC 2013
The big news here is the removal of MySQL in favor of MariaDB. This
shouldn't really be a surprise on any level. The poll on LQ showed a large
majority of our users were in favor of the change. It's my belief that
the MariaDB Foundation will do a better job with the code, be more
responsive to security concerns, and be more willing to work with the
open source community. And while I don't think there is currently any
issue with MySQL's licensing of the community edition for commercial uses,
several threads on LQ showed that there is confusion about this, whereas
with MariaDB the freedom to use the software is quite clear. Thanks are
due to Heinz Wiesinger for his work on transitioning the build script,
testing, and getting us all behind this move. He's been working with
MariaDB (and their developers) for several years now. Vincent Batts also
had a hand in the early discussions here -- he met Daniel Bartholomew of
MariaDB on a train last year and got a copy of the source to play with to
pass the time on the journey (ah, the miracle of thumbdrives :), and was
impressed with not only MariaDB itself, but also with the welcome that
Slackware was getting. We expect they'll be responsive to any concerns
we have. In the vast majority of situations, MariaDB is entirely
compatible with existing MySQL databases and will drop right in with no
changes required. There's an article available outlining the areas in
which MariaDB differs from MySQL that I'd recommend reading:
https://kb.askmonty.org/v/mariadb-versus-mysql-compatibility/
Thanks to the MariaDB Foundation! We look forward to working with you.
ap/mariadb-5.5.30-x86_64-1.txz: Added.
ap/mysql-5.5.29-x86_64-1.txz: Removed.