Silverlight is a new cross-browser, cross-platform implementation of the .NET Framework for building and delivering the next generation of media experiences and Rich Interactive Applications(RIA) for the web. It runs in all popular browsers, including Microsoft Internet Explorer, Mozilla Firefox, Apple Safari, Opera. The plugin required to run Silverlight is very small in size hence gets installed very quickly.
It is combination of different technolgoies into a single development platform that allows you to select tools and the programming language you want to use. Silverlight integrates seamlessly with your existing Javascript and ASP.NET AJAX code to complement functionality which you have already created.
Silverlight aims to compete with Adobe Flash and the presentation components of Ajax. It also competes with Sun Microsystems' JavaFX, which was launched a few days after Silverlight.
You can not compare them. Just like AJAX, it is just an enhancement in the .net. Silverlight enables development of the next generation of Microsoft .NET-based media experiences and rich interactive applications (RIAs) for the Web. Silverlight is delivered as a cross-platform and cross-browser plug-in that exposes a programming framework and features that are a subset of the .NET Framework and Windows Presentation Foundation (WPF).