I believe that your first sample actually creates an anonymous function that is able to take on many different signatures whose body is the single statement Console.WriteLine.... Because it can match different signatures, it does not cause a problem. In the second sample, the lambda syntax itself defines a function that takes no parameters with the same body. Obviously the latter is not consistent with the defined Action so you get the error.
C# Anonymous Method Reference
There is one case in which an
anonymous method provides
functionality not found in lambda
expressions. Anonymous methods enable
you to omit the parameter list, and
this means that an anonymous method
can be converted to delegates with a
variety of signatures. This is not
possible with lambda expressions.