Based upon recent evidence from abundance patterns of chemical elements in solar energetic particles (SEPs), and, ironically, the belated inclusion of H and He, we can distinguish four basic SEP populations: (1) SEP1 -pure "impulsive" SEPs are produced by magnetic reconnection in solar jets showing steep power-law enhancements of 1≤ Z ≤ 56 ions versus charge-to-mass ratio A/Q from a ≈3 MK plasma.(2) SEP2ambient ions, mostly protons, plus SEP1 ions reaccelerated by the shock wave driven by the narrow coronal mass ejection (CME) from the same jet. (3) SEP3 -a "gradual" SEP event is produced when a moderately fast, wide CME-driven shock wave barely accelerates ambient protons while preferentially accelerating accumulated remnant SEP1 ions from an active region fed by multiple jets. (4) SEP4 -a gradual SEP event is produced when a very fast, wide CME-driven shock wave is completely dominated by ambient coronal seed population of 0.8 -1.8 MK plasma usually producing a full power law vs. A/Q for 1≤ Z ≤ 56 ions. We begin with element abundances in the photosphere that are fractionated during transport up to the corona based upon their first ionization potential (FIP); this important "FIP effect" for SEPs provides our reference abundances and is different for SEPs from that for the solar wind. We then show evidence for each of the processes of acceleration, reacceleration, and transport that conspire to produce the four abundances patterns we distinguish.