What is the difference between infranuclear and supranuclear paralysis?

Different types. Supranuclear refers to loss of function due to a lack of high level cerebral control of a cranial nerve. E.G., in supranuclear gaze paresis there is difficulty voluntarily moving the eyes, but reflex eye movements are intact. Nuclear/ infranuclear refers to problems caused by damage to a cranial nerve nucleus or nerve itself. In this case voluntary & reflex movements would be impaired.