I have now got Netbeans 7 and have previously on my work machine gone to services, right clicked databases "New Connection" and then chosen finish and BOOM I have a database I can send to, open and close which is all very nice.
Now at home I have no list of databases and when I right click "New Connection" I get this fabulous notification
cannot establish a connection to jdbc:mysql://localhost:3306/mysql using com.mysql.jdbc.Driver (Communications link failure The last packet sent successfully to the server was 0 milliseconds ago. The driver has not received any packets from the server.)
I guess that, despite your apparent total approval of the situation, you really have a question?
It appears that somebody configured your work machine with links to some MySQL server somewhere. You're going to have to do the same thing to your home machine.
(And this isn't anything to do with Java programming. You haven't even got there yet. You're still trying to configure your Netbeans environment. So let me move this post to the forum which is about Netbeans.)