To answer your question you need to understand what .net actually is.
The .net framework is a huge bunch of classes installed on your operating system. It acts as a layer between your coding and your operating system.
ASP.net is not a coding language. It is a term to describe the (vast) area of the .net framework that allows you to write code directed to the web. The .net framework is chopped up into categories called namespaces. A typical namespace that would be described as to do with asp.net would be XML.
VB.net is different. It is one of several code languages that can communicate with the framework. Others include c# or j#. Cool thing is, is that your code, whatever language you use, gets compiled down into the same intermediate language (IL) which communicates with the .net framework.
So asp.net is a descriptive term for an area of the .net framework
vb.net is one of several code languages that is compatible with the .net framework.
asp.net includes the use of events but they are not as extensive as say a windows .net application because of the limitations of web browsers.