No, because a Markov process only depends on current state. All Markov processes are stateful systems, but not all stateful systems are Markov processes.

For example, an exponential moving average:

    s_n+1 = a x_n + (1 - a) s_n 
      y_n = s_n

    where a, x, s, y in Reals

The next state depends on all past state, including initial conditions.

Conceptually, stateful systems are the notion "where I am going depends on where I am." Markov processes are stateful systems where "where I am going depends on where I am, but not upon where I came from."