This is probably one of those embarrassingly simple questions, but here goes. Consider the following two constructs:
CSPRNG made out of a block cipher (AES) with a counter such as
CSPRNG made out of a secure hash function with a counter (Java SecureRandom's SHA1PRNG) such as
The common denominator is the provision of a counter. What's the point of the counter as you could simply do state' = F(state) once you have state established? So the state would be the seed alone, and it would be iteratively processed to produce the random stream. What does the counter bring to the party?