Does "service mysql start" start the mysql server or client?

I have done as much searching on this topic as I can, and the answers do seem all over the place. Some sites state that the "service mysql start" starts the server, while others state that one must use "service mysqld start": e.g.: <http://theos.in/desktop-linux/tip-that-matters/how-do-i-restart-mysql-server/>

To elaborate some more - my understanding is that "mysql" is the process that represents the client interface that connects to a mysql server (either remote or local) and "mysqld" is the process for the server. I would assume that "service mysql start" would only start the mysql client (not the server) and I can use this client to connect to any mysql server. And if I haven't used "service mysqld start", no server would have been started on the local host and therefore I can't use the mysql client to connect to any local mysql server. Is my understanding correct?

Also, I am using a Red Hat server.

Any clarifications and explanations most appreciated - Thanks!