I've got my biases, but whenever something like this comes up, I just make some popcorn and enjoy the show.
In MySQL the backslash sequences are commands to the mysql client for things that are implemented in the client and have to do solely with the command line client software. These things are not available using other clients. Vs things like listing columns and databases and functions have their own DDL language constructs entries and are queries in their own right that can be sent by any client software to the server and return iteratable results. MySQL is more like Oracle in this regard.
That distinction isn't obvious in psql and that contributes to a larger hurdle when using the command line client. This makes psql attractive to power users, as there are a lot of shortcuts for things that might require longer DDL statements to be typed or queries against information_schema.
https://dev.mysql.com/doc/refman/5.6/en/mysql-commands.html