Wondering implies a state of curiosity or uncertainty, often involving a desire to know or understand something. It is closely associated with mental processes like pondering, questioning, and seeking answers.
Wandering refers to physical movement without a specific destination or purpose. It doesn't typically relate to thinking or mental processes.
Here are some examples:
* Wondering: "I was wondering what you thought of the movie."
* Wandering: "I wandered through the forest, lost in thought."
In summary, "wondering" is the correct word when you're talking about thinking, while "wandering" is used for physical movement.