ASP (Active Server Pages) is the older of the two technologies. ASP uses VBScript or JScript which are interpreted languages.

ASP.NET uses a framework that uses many more langugages (VB, C#, J# ..) and is much more Object Oriented and type safe. and has a cleaner division between client and server code and has built in libraries for some of the latest Internet technlogies such as XML, AJAX and Web Services etc.

I would say ASP and ASP.NET are *very* different in almost every way.