What is the difference between a lazy eye or a strabismus eye?

Lazy eye: They mean the same. The terms both refer to a defective eye muscle.

Alignment/vision: Strabismus is a simple failure of the eyes to line up & focus on the same point.There are several potential causes. Over time this might lead to lazy eye (amblyopia) where the brain decides to turn off the input of one eye if the images don't line up or one is fuzzier than the other. The "lazy eye" can sometimes be improved if alignment or weakness are fixed early, but may be permanent.

Yes: Lazy eye (amblyopia) may occur without any evidence of strabismus.

Yes: Strabismus is the generic term for eyes that are out of alignment. A consequence of this in some cases is the popular term 'lazy eye' which indicates an eye which might drift out of alignment or an eye with lowered vision that cannot be improved (termed amblyopia). Not all lazy eyes are out of alignment but usually if the misalignment persists, one eye will become lowered in vision ('lazy').

A lot: Strabismus is the term used when the eyes do not move exactly synchronously. It is accompanied by double vision. If it is not corrected the brain ignores one of the images and in time we have a lazy eye(meaning the eye has little or no vision).

Eye function: Lazy eye is a lay term usually used to designate the vision loss that occurs when the brain turns off the eye input because it is fuzzy or misaligned (double vision). We call it amblyopia. Strabismus is a label used when the eyes don't line up and focus on the same object. Some lay people use lazy eye for both issues.