A lazy eye is actually one that wanders at times and is not in a fixed position(thus lazy), quite often they are controllable because they are just ‘tired’ when forced to remain in one position and the person with that disability can just keep looking around to keep their eye from getting tired of being stuck in place. Wall-eye or Cross-eye is when the eye is stuck in a position looking out from or in-to the center of vision.

It doesn’t necessarily have to be lazy eye.

My son had a similar problem growing up (not as bad), because he had a fold in his retina which obscured his vision straight-on and his eye was always trying to tic sideways so he could see past it.

Or there’s Marty Feldman, whose wall-eye was a result of an illness later exacerbated by a head injury.