There are 2 licences here - server and cal

Server allows you to install the binaries on a server - cals allow users
to connect to servers

For each server you deploy you need a server license

If you are using a separate server for the internet  facing sites  then
you will need a separate server license

Anyone connecting over the internet to the internet facing server will
be covered by the internet sites license

Internal users connecting to any server will be covered by the internal
cals

Depending on your licensing scheme when you install the server binaries
you may use the same or different license keys (select and ea will be
the same, Open and boxed will be different)

I still need a bit more clarification:

All of our licenses  are under the Select licensing program. When we
installed MOSS 2007 for our intranet about 4 months ago, we used a
license key and the media we received upon purchase.

However, when we purchased the SharePoint for Internet Sites license
(Select), we did NOT receive new media or a new key (as far as I can
tell on the MS Licensing site). So, I am sitting here wondering if I'm
missing something.

Do I use the same media I received 4 months ago (MOSS 2007) and the
same key? Should I have received new media and a new key? Or, should
I have received just a new key?

The media and license are to install the server binaries

You don't get a license key for the cal (client connections) - its just
the agreement that allows them to connect

You wont get new media or key - if you want internet  people to connect
to a different physical server running an additional copy of moss  you
need to pay for another server license - if they are going to connect to
the same server as your internal people you don't need any additional
server licences and your internet license covers you for their
connections