Should both mysqld_safe and mysqld be running at the same time on startup?

On launching my CentOS VPS (setup by someone else), MySQL starts two processes on boot:

mysql : /usr/libexec/mysqld --basedir=/usr --datadir=/var/lib/mysql --user=mysql
root: /bin/sh /usr/bin/mysqld_safe --datadir=/var/lib/mysql --socket=/var/lib/mysql/mysql.

Is this normal / the correct way to setup MySQL (that root is running mysqld_safe?)

Thanks!

Yes, that's the way it's supposed to be. mysqld_safe spawns a mysql-user run daemon (mysqld).

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