What is the difference between amblyopia(lazy eye) and strabismus(cross eyed)?

They can be mutual!: Amblyopia results from the brain not learning how to use the information from the eye. Sources of that may be refraction (glasses), deprivation (eye covered by droopy eyelid), or strabismus (misaligned eye). There are many patient with perfectly aligned eyes that have amblyopia, and many with strabismus that have no amblyopia...

Big diffrence: Crossed eyes, may result in amblyopia of the eye less used. The brain will mask the image form that eye so patient doesn't see double. Crossed eyes in children less than 2 years old need to be straightened as soon as possible after reasonable amblyopia therapy if present. If eyes are straightened before age 2 3d visison usually develops. Between 2-4 it drops significantly. >4 not possible.

Different definition: Amblyopia is when the brain starts to turn one eye off and therefore it sees worse than the other eye. Strabismus is just a misalignment of the eyes. Often, strabismus can lead to amblyopia, but can occur without it. Amblyopia can occur without strabismus.