We present a novel robot end-effector for gripping and haptic exploration. Tactile sensing through suction flow monitoring is applied to a new suction cup design that contains multiple chambers for air flow. Each chamber connects with its own remote pressure transducer, which enables both absolute and differential pressure measures between chambers. By changing the overall vacuum applied to this smart suction cup, it can perform different functions such as gentle haptic exploration (low pressure) and monitoring breaks in the seal during strong astrictive gripping (high pressure). Haptic exploration of surfaces through sliding and palpation can guide the selection of suction grasp locations and help to identify the local surface geometry. During suction gripping, this design localizes breaks in the suction seal between four quadrants with up to 97% accuracy and detects breaks in the suction seal early enough to avoid total grasp failure.