Generally speaking these expressions seem synonymous and more or less interchangeable, but they might also be used to emphasize slightly different things. Being able to focus sounds more like a faculty (”mind’s eye”) whereas being able to concentrate could be seen more like a learnable skill. And ”wandering mind” sounds more like a symptom whereas the other two point to a cause.
One can let one's mind wander, but one may still retain the ability to focus or concentrate if one so chooses. Sometimes one can lose one's thought or one's train of thought if one is interrupted or distracted, but that can happen without one's mind wandering off on a tangent; indeed one's mind may very well concentrate on attempting to recover the lost thought or train of thought. To lose one's mind is just to go insane, but it is often said as a hyperbole.
PS. "Losing one's thought" ≠ "being lost in thought". One can be lost in thought without losing one's thought.