Jerking eye movements? = nystagmus?

Most commonly, yes. Nystagmus is the name for usually rhythmic, oscillating (back and forth, or up and down) involuntary movements of both eyes. It is most often seen as a congenital (born with) finding, or develops shortly after birth. There are other causes for unusual or "jerking" eye movements too, and affected individual should be seen by an ophthalmologist, neuro-ophthalmologist, or neurologist for a diagnosis.