(these are the main ones at least)
MySQL is open-source. People, usually former MySQL employees, have branched off of the open source MySQL codebase with their own versions, usually offering some degree of compatibility with the original product. From my experience, MariaDB and PerconaDB are forks that can be considered drop in replacements for MySQL while adding functionality and performance.
This is the original MySQL database as well as new development since Oracle’s purchase of the product. There is still a “community” edition however Oracle seems committed to differentiating community(free for non-embeded uses) and enterprise(the one you always pay for) licenses by concentrating its development of advanced features included in the enterprise version. The community edition is just as good if not better than its ever been however do not expect modern “big-data” style enhancements to come from Oracle for free in the future. Basically, if you are dealing with 20 million rows or less in your largest tables and don’t expect to need advanced features such as clustering or raw backups, the original community edition of this product as Oracle offers it is a fine way to go. Anything beyond this will require either an investment in Oracle Enterprise technology or consideration of another fork.
Drizzle is open source and was forked from the 6.0 development branch of the MySQL. It has a client/server architecture and works with standard SQL. Drizzle is distributed under the the GNU General Public License with certain drivers and such issued under the BSD license.
MariaDB is a fork designed to offer a higher performance drop in replacement for the MySQL product offered by Oracle. I would say it is best know for its advanced query optimizer which really speeds things up on certain types of queries without the user really having to worry about what has changed. It was forked by some of the original developers of MySQL who were worried about how the Oracle acquisition would turn out. The plan for Maria is to strive for as high of a level of compatibility as possible including all commands and functions. While you can use InnoDB with Maria, the default storage engine is Percona’s XtraDB which offers quite a few performance enhancements and fixes for particular types of queries that InnoDB did not seem to like.
Percona Server is another fork aiming for high compatibility with official MySQL releases. In addition, they have focused on performance enhancements and monitoring tools to aid in administration and query optimization. Like MariaDB, Percona server uses XtraDB. Percona generously offers for free lots of scaling, monitoring and backup tools rivalling Oracle’s enterprise level products which are, of course, not free. My usual product choice as of late for a 1-node product is to install MariaDB with XtraDB tables and using Percona enterprise tools against it when needed for optimization and replication.
WebScaleSQL is a branch developed in a partnership between Facebook, Google, LinkedIn and Twitter for the purpose of handling very large scale data sets horizontally scaled across ridiculous amounts of commodity hardware. All of these companies being faced with similar challenges were wise to pool their efforts in the development of this branch. WebScale is also GNU and you can access the source on github.