The difference is arbitrary but fixed. For any given Markov model, there are inputs that can fully fit in the present state and inputs that can't. But for any given input, there are models that can encode it entirely in the present state.
Markov models are useful for understanding the limitations of any specific next-token predictor with a fixed context window. But not for the limitations of such predictors in general, as there is always a Markov model large enough to handle any specific input.
Markov models are useful for understanding the limitations of any specific next-token predictor with a fixed context window. But not for the limitations of such predictors in general, as there is always a Markov model large enough to handle any specific input.