asp.net is sucessor to asp. asp was a set of tools for IIS the web server in windows OS that used vbscript (not VBA, but very similar) to create dynamic web pages, often by calling databases through oledb.
asp.net isn;t just a new version of asp, but a total rework (as vb.net, is not vb). asp.net can be written in any .net language, usually vb.net or C#, and has many built in controls for handling features such as user registration and login, retrieving and updating database or xml data, validating form data (both in browser through javascript and on the server side in events).
asp.net is alot like vb.net. if you place a few button on a web page, the code view with have onclick and other events for each button. When viewed in browser , clicking a button sends a "postback" (a call to the same webpage, but with relevant changes included in the post data), which then causes the webserver to execute the appropriate code.