You've posted an almost identical question before already. The issue is, if you want some specific examples, you will need to cite functionality you wish to incorporate. I cannot begin to go down each class in .NET and explain the differences, let alone wish to.
The similiarities between VB .NET for desktop applications and ASP .NET end at code similiarity. The way they handle the code is quite different. VB .NET can deal with user input immediately, and only has to deal with ONE user. ASP .NET you need to keep in mind that everything is hosted on a server, and you could have thousands at any given time. In addition, it can only deal with information once sent back to the server.
With that in mind, your previous post concerning MVC design is perfect. Keep in mind though, the implementation of the back end will be drastically different, BUT how that back end functions should be identical.