To wander is to move about with no destination or purpose. Wandering is a physical activity, though the word is sometimes used figuratively for nonphysical actions that are aimless (e.g., a movie or a conversation might wander). To wonder is to feel curiosity, to be in doubt, or to have a feeling of admiration. The verb also bears the less commonly used sense to have a feeling of awe—e.g., she wondered at the beautiful scene outside the window. In either sense, wondering is a mental activity.
The words have separate origins in Old English. Wonder comes from wunder, a noun for a marvel or a wondrous thing.1 Wander comes from wandrian, meaning to move aimlessly.1 They took their modern forms by the 16th century (both words appear in Shakespeare), and they have remained more or less unchanged through the centuries.
Yet many inside and outside the force wonder whether the pileup of scandals and his increasingly authoritarian use of power have diminished his once-towering stature. [New York Times]
I have a deep-seated need for love but I don’t often wander around Tesco looking for it. [Guardian]
For years I’ve wondered what goes on behind the doors of a Buddhist temple. [National Post]
At the worst of it, he found himself wandering in a park alone, mumbling to himself. [Stuff.co.nz]