Does the Markov assumption say that the conditional probability of the next state only depends on the current state or does it say that the conditional probability depends on a fixed finite number of previous states?
As far as I understand from the related Wikipedia article, the probability of the next state $s'$ to appear only depends on the current state $s$.
However, in the book "Artificial Intelligence: A Modern Approach" by Russell and Norvig, on page 568, they say: "Markov assumption — that the current state depends on only a finite fixed number of previous states".
To me, the second statement seems contradictory to the first, because it may mean that a state can depend on the history of states as long as the number is fixed a finite. For example, the current state depended on the last state and the state before the last state, which is 2 sequential previous states (a finite number of states).
Is Markov assumption and Markov property the same?