This deals witth C# and .NET 4 becuse I am making an app using these two. But I am using WPF.

I was working with a WPF application and I decided that the controls and graphics I wanted to display on the grid might look better if it was a silverlight component.

I thought this way because of all the cool silverlight controls that look very flash-like.

But now that I have gottem my Visual Studio 2010 set up with SIlverlight, it seems that every silverlight app I can make are ASP.NET in nature. It seems that instead of a cool
GUI control to make, Silverlight is telling me that it is primarely a dataflow sort of application for the web.

What is the relationship, if any, between WPF and Silverlight? Can I or can I not put a silverlight control into my existing WPF application?

You can make your controls look flashy with WPF as well :-)
Silverlight had the Beta code-name WPF/E for "WPF everywhere". You have more options to run your applications with Silverlight, you can use different browsers and different platforms, and the complete framework is not needed, just an add-in.
With WPF you have more features available, but it requires the .NET framework installed on the client system.

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