At first look, Seaside doesn't look much different than ASP.NET. It's all about modelling your application's interface in terms of objects and methods ("messages" for you Smalltalkers). Pages are built up of components, inheriting from System.Web.UI.Control (ASP.Net) or WAComponent (Seaside) that can include other components. When the user does things with any component, it results in events being fired (ASP.NET) or messages being sent (Seaside). Both frameworks seem to strive to abstract away the request/response nature of the web, and to allow the programmer to use a more event-driven approach to developement. In addition, seaside uses at it uses continuations to make it possible to, for example, ask the user something (similar to how a modal dialog would do it in a normal GUI enviroment), and then do something with the provided answer -- all within the context of a method.
The main difference is that programming in the Seaside framework results in a lot less housekeeping code. The object is really a ordinary object, except that it's executed through the web. The difference didn't really dawn on me before I tried to recreate WACounter as a ASP.Net Server component -- it did involve a whole lot of code to handle events, manage viewstate and so on.
It's cool that people are finding out about Seaside and what it can do.