We present X-ray spectral analysis of 20 point-like X-ray sources detected in Chandra Planetary Nebula Survey observations of 59 planetary nebulae (PNe) in the solar neighborhood. Most of these 20 detections are associated with luminous central stars within relatively young, compact nebulae. The vast majority of these point-like X-ray-emitting sources at PN cores display relatively "hard" (>=0.5 keV) X-ray emission components that are unlikely to be due to photospheric emission from the hot central stars (CSPN). Instead, we demonstrate that these sources are well modeled by optically thin thermal plasmas. From the plasma properties, we identify two classes of CSPN X-ray emission: (1) high-temperature plasmas with X-ray luminosities, L X, that appear uncorrelated with the CSPN bolometric luminosity, L bol and (2) lower-temperature plasmas with L X/L bol ~ 10–7. We suggest these two classes correspond to the physical processes of magnetically active binary companions and self-shocking stellar winds, respectively. In many cases this conclusion is supported by corroborative multiwavelength evidence for the wind and binary properties of the PN central stars. By thus honing in on the origins of X-ray emission from PN central stars, we enhance the ability of CSPN X-ray sources to constrain models of PN shaping that invoke wind interactions and binarity.