I am a total newb when it comes to either, so can I run a test page to see if the server is running one or either?
Also, in PHP I usually use an include statement to include files that contain common elements like menus or footers. Is there a similar statement in ASP?
That way of doing includes is very old. A lot better way of doing it is to create a UserControl and insert that on you page. It is a .ascx file. Then you also have something called a Master Page. Which usually contains your sites header, menus and footer. With a content section or more depending on your needs. Then each aspx page points to the master and you put your code into those content blocks declared on the master page.
If the site has an asp extension, it is probably ASP. If it has a /bin folder with some .dll files, it is probably .NET. Server generally is capable of running both.
That is all fine and good – if you want to know what version of .NET the computer with that instance of IE is running. It won’t tell you in any way what the server is running.