During emergence from general anesthesia, a 52-year-old male patient recovering from open cholecystectomy shows irregular, jerky respirations with increased muscle tone and begins to move purposelessly. The anesthesiologist notes that the corneal reflex has returned but the pupil remains dilated. Which stage of Guedel's classification is this patient transitioning through, and what is the most important clinical difference between this stage during induction versus emergence?