The "distributed" part. While distributed could mean a lot of different things, I'm guessing the OP wants either horizontal scalability, or bidirectional repli

The "distributed" part. While distributed could mean a lot of different things, I'm guessing the OP wants either horizontal scalability, or bidirectional replication between multiple regions/datacenters. And while it's technically possible to do those with mysql or PostgreSQL, they definitely don't work out of the box, and require a lot of careful architecting, and it isn't really how they were originally designed to be used.