There's a difference between an instance of a type and a type's 'type object' which I suspect is what you're getting at here.
When a type (including a static class) is first accessed in an AppDomain, the CLR creates an instance of System.RuntimeType which is an internal class which inherits from the abstract System.Type class. This instance contains information about the type and there's only ever one of them for a given type. When you call typeof(SomeType) or various GetType() methods, it's a reference to this 'type object' which gets returned.
An instance of a reference type, on the other hand, is (in effect) a block of memory on the heap which contains a reference to its type object, a sync block index and space to store its instance fields.
The point I'm making is that there are never any instances of the static class itself in constrast to a singleton which has exactly one instance. However, there are type objects for both static classes and singleton classes.