Not quite.

 

Take your wayback-machine back to 2005 when WPF was announced: there was WPF and WPF/E, which was a cut-down version of WPF which was renamed Silverlight in 2006. Fact is WPF and Silverlight share a lot of code, it's more the front-end stuff that's different (WPF uses D3D, Silverlight is 2D) but the rest is verrrry similar.

 

...unless you're talking about the Silverlight runtime environment, which is kind of a compact-compact-framework.

 

So yes, there's overlap, but less than you'd think.