What's the difference between wOnder & wAnder?

This is a tricky one because the difference in pronunciation is minuscule.  As a result, many ESL students have difficulty in detecting the correct word, as well as pronouncing it.  Let's take a look at each.

WONDER

The "o" in wonder sounds like "uh" as in the word "fun."  The meaning is to think or imagine something.

Ex. I wonder what she's doing right now... Is she thinking about me?"

WANDER 

The "a" in wander is like the sound "ah" as in the word "walk."  To wander means that you have no destination or that maybe you're lost or that you have no particular place to go and instead you prefer to take any direction or way that you choose spontaneously.

We often use this word with the preposition "around."

Ex.  Instead of using the map, we preferred to wander around the quaint neighborhood of El Born in Barcelona.

I hope this makes it clear for you!