Not sure about ecliptic, never used it. local is vessel-local relative, i.e. your vessel is at 0 0 0 of the coordinate system and facing towards 0 0 1.
Global is the "root" coordinate system of the engine. 0 0 0 is the barrycenter of the system (inside the sun, but usually not the exact position of the sun), and the origin of the orientation is pretty much irrelevant.
There's functions like localToGlobal and globalToLocal in the SDK to convert between the two. Assuming this *is* an SDK/Programing question, which you never mention, but I can't quite imagine what non-programing related thing you might need to convert between the coordinate systems for. You certainly don't need to understand them in order to fly, the MFD projections are more important there.