ASP was microsofts first attempt at a web framework. It is now very outdated.
The is little in common between ASP and ASP.NET apart from a couple of object names.
They are totally different technologies, ASP basically is a scipting engine; you do not compile code into exe's or dll's, this makes it quite slow.
The improvements in ASP.NET are:
1. Compiled code (into exe's and dll's) offering much better performance
2. Programmable controls (you don't have to write every last bit oh HTML and code)
3. Markup is XML-based
4. ASP.NET comes with several ready built frequently used controls e.g. user authentication, file upload, banner rotation e.t.c.
5. Several built in security checks
Look up (but don't get distracted by) the following ASP.NET attributes.
1. Event driven programming
2. object oriented consepts
A good place to start learing ASP.NET is http://asp.net