Isn't this done through Alternate Access Mapping? Where you have two different
paths into the same site/content db.....

AAMs work if you are trying to provide two paths to the same content yes. The
other question is, is he trying to have two separate sites? In which case you
need two separate web applications, the host headers for them and DNS
resolution. It sounds like he is unfamiliar with Host headers and how they work.

In order to have two different URLs on the same server  that serve up different
content you need to provide different host headers for the two sites. Each one
needs its own web application in SharePoint (let's not go down the vanity URL at
this time, keeping it basic). When you create the web app you provide the
appropriate host header, such as testsrv and mymoss. You also need the
corresponding DNS entries for both hosts so that they can be resolved.

Based on the question (he mentions multiple site collections) (create another application with corresponding host
headers).