They are in many ways the same although I'd be more inclined to use 'wander' if I was unfamiliar with the area. For example if I've just arrived somewhere on holiday I might say to my friends/family "I'm going to go for a little wander".
stroll is more of a leisurely walk while wander is a walk without a fixed course or destination. for example, Peter strolled down the street with his little sister. Peter and his little sister went outside to wander around until it was time to go.