I see a lot of people claiming that these two verbs really mean the same thing always or are used interchangeably, but I'm not sure about it because I think two words can share the same meaning for a certain context (i.e they can be synonyms)- but in some cases one communicates the idea better than the other. So, what's the difference between "to stroll" and "to wander"?
To stroll is to walk in a leisurely way, and the focus is on the mode of travel. To wander is to walk or run, at any speed, without a fixed course or destination, and the focus is on that. You can stroll with a destination in mind, or not. If you stroll aimlessly you are wandering.
The verbs may be used together, and often can be interchanged, depending on the emphasis intended:
I wandered around the park, strolling from tree to tree.
I strolled around the park, wandering from tree to tree.
"Stroll" is about speed. "Wander" is about direction.
To stroll is to walk slowly, or as a noun, a stroll is a gentle hike.
We strolled from the town centre back to my home, chatting all the way.
If you wander, you don't walk straight.
We wandered through the forest, sometimes following the stream, sometimes walking away from it.
Both imply that you are not walking urgently, and often you would wander at a strolling pace, or while you are on a stroll, you would tend to wander.