SP Alternate Access Mapping question - trying to understand what _should_ happen and what _could_ be done

We have a test server - let's call it "testserver". On it, SP 2010 is installed. The intended farm name for this machine is "testfarm".  A DNS exists for testserver with testfarm as an alias.

The following AAMs are created:

Internal URL                                          Zone                              Public URL for Zone

http://testfarm                                      Default                          http://testfarm

http://testfarm.internal.primary.domain  Intranet                         http://testfarm.internal.primary.domain

http://testserver                                    Internet                        http://testserver

The first of these 3 AAMs are working.  The last two of these display an IIS screen rather than the SharePoint.

While I don't really like people using the server name, in other farms here I have seen that work fine.

However, certainly I would have expected the second AAM to work.

I am obviously not understanding how something needs to be set up. Is there something simple that I have forgotten to set?

Thank you for any help you might provide.