What is the difference between XBAP and Silverlight and when should i use which of these technologies?
Let me step back and start with a precursor:
In .NET 3.0 we have Windows Presentation Foundation (WPF) which allows us to create stunning UIs for desktop applications using managed code. If you still haven't experienced the power of WPF check out the WPF applications here.
Now the logical question was "How can we take the same stunning experience onto the web" - the first step towards that was XBAP - XAML Browser Application (XAML is eXtensible Application Markup Language - an XML type markup to store the UI). XBAPs allow you to run Rich Internet Applications that look and function like WPF desktop applications. These XBAPs run inside the Internet Explorer in a separate sandbox to prevent applications from accessing resources on the local system. A restriction on XBAPs is that they need .NET framework 3.0 or higher to be installed on the client machine to run.
This is exactly what Silverlight is for. So if you want your application to be available on the internet and not dependent on the .NET framework, Silverlight is the way to go. Silverlight is a cross platform, cross browser plugin that allows you to run UIs defined in XAML inside the browser. Silverlight supports a subset of XAML as of now.
I hope this clarifies some of the doubts around XBAP and Silverlight. Feel free to leave questions if you have any.