This study aims to classify and compare AC and DC partial discharge (PD) based on PD pulse waveform analysis. To achieve this goal, we designed a testbed that enables precise measurements of individual PD pulses. The testbed is used for collecting data from four different types of PDs including cavity, surface, corona, and floating potential discharges generated by individual PD source samples. All samples were examined under AC, positive DC, and negative DC electrical stresses, through which we captured thousands of PD pulses. We classify the waveforms of each PD type into representative groups associated to their discharge mechanisms. The statistical data of the measured pulses are utilized to identify the differences between AC and DC PDs while the clustered patterns of PD amplitude versus their temporal characteristics serve as a means to classify the types of PDs under AC and DC electrical stresses.