By my definition, a Colpitts oscillator uses two capacitors in-series to create a "center-tap", while a Hartley oscillator actually has a tap on the coil (three leads). The tap connection is used to create either (1) a step-up in voltage with no phase reversal, or (2) a 180 degree phase reversal. This comes from the Barkhausen Criterion, which is the basis of all oscillators.
(1) is used with a common-collector/drain or a common-base/drain oscillator like your second circuit. (2) is used with a common-emitter/source circuit like your first circuit.