just a nitpick: MySQL comes with the same default engine (InnoDB) for at least 10 years now. It is recommended by docs and it is what everyone uses unless they go out of their way to install some very specialized storage engine.
In my years of consulting I have yet to see someone not using just InnoDB in MySQL.
MySQL is a bunch of different engines that share a meaningful subset of SQL.
Somehow, Postgres got more popular lately, probably because it makes migrating from Oracle easier.