I did rpm -qa | grep ftp and got:
gftp-2.0.14-4mdk
proftpd-1.2.7-1mdk
ftp-client-krb5-1.2.7-1mdk
lftp-2.6.4-2mdk

Do I have a ftp server? Or is it a ftp daemon that I should have? How do I start it/stop it?

yes, you have proftpd running. I just spent days trying to figure all this out and basically, you have a daemon which is the proftp daemon. How this runs is a slightly more complicated issue but it's not hard. Whenever the daemon is running and assuming you do not have a firewall blocking traffic (need to check cause red hat comes with built in firewall rules) (iptables -L) then you have a ftp server running. The way you run this daemon is probably in your inetd.conf file located in /etc/ which means it will be ran from your inet daemon at startup. Then you will also have a proftpd.conf file which specifies all your option and bells and whistles you want your ftp server to do. I personally got rid of the proftpd and installed vsftpd which seems like a better ftp server. However, i am running slack9 so this took some more work because i had to do it from source. If you have red hat then it is easy cause you can use the rpm. Anyway, that is all there is to ftp servers. As for how to stop this daemon you can just do a ps aux | grep ftp and get the PID (first column i think) and then do a kill -a 'PID'

Okay, I have proftpd installed. Good.
Now, I edited /etc/xinetd.d/proftpd-xinetd to look like this:

service ftp
{
disable = no
socket_type = stream
wait = no
user = root
server = /usr/sbin/in.ftpd
log_on_success += DURATION USERID
log_on_failure += USERID
nice = 10
}

I then restarted xinetd:
/etc/rc.d/init.d/xinetd restart

I then tried to ftp localhost:
Connected to localhost.
421 Service not available, remote server has closed connection
ftp>

So, I'm at a loss. What's wrong?

What does "tail /var/log/messages" say after the xinetd restart?