MySQL root/host passwords
 

After installing MySQL, it tells me to set the root password using...

./bin/mysqladmin -u root password 'new-password'
./bin/mysqladmin -u root -h $HOSTNAME password 'new-password'

Are these the same?

After starting the mysql.server, I ran the first command to set my root password and it worked. However, when I try to run the second command (w/ the -p option), it prompts me for my password. I then enter in the password I set on the first command, but it errors out w/ the following...

./bin/mysqladmin: connect to server at 'host' failed
error: 'Access denied for user: 'root@host' (Using password: YES)'

Am I doing circles here or is something bigger going wrong?

use mysqladmin -h localhost