Strong markov property vs usual markov property.

I was trying to understand the difference between strong Markov property and the usual Markov property for a discrete number of states. I think I understand why the strong Markov property implies the usual one : We have to consider a deterministic stopping time $$T(\omega)=t_0$$, right?
But what would be a simple example (like coin toss, dice toss,...) where we have the Markov property but not the strong Markov property?