I would like to use the async keywords in a project that is created in .net 4.0.
If I go to the nuget.org website and I look for "async", i many results, but mainly I get this:
Visual Studio Async CTP (Version 3, Unofficial) 0.3.0
Which is the differences between both of them?

You want the Microsoft.Bcl.Async package. That's a properly released, non-CTP package that is stable. This also requires VS2012 since an updated compiler is needed to understand async and await.
In theory one could use older tools from VS2010 along with the older CTP library, I'd strongly recommend that you don't - it has bugs and the installation itself is a hit-or-miss.
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