The ASP.NET Ajax Extensions are set of Ajax-based controls that work in ASP.NET 2 (or above) based applications.
Ofcourse,they also need the Ajax runtime which is actually the Ajax Framework 1.0.
ASP.NET Ajax Extensions 1.0 have to be downloaded to run with ASP.NET 2.0
The new ASP.NET 3.5 Framework comes with the Ajax Library 3.5 (containing the Ajax Extensions 3.5). So in order to use the latest Ajax, simply download .NET 3.5 Framework. Summary :
ASP.NET Ajax Extensions 1.0 -> For ASP.NET 2.0
ASP.NET Ajax Extensions 3.5 -> For ASP.NET 3.5