With my selfMOC having control over the whole electromagnetic spectrum (lightning, plasma, and magnetism), I've thought about this a lot.
In my heacanon, lightning (his natural element) is pure electricity, which he can use to shock enemies, and (with his extended powers) control the electrical components of MU beings. More electricity than the actual "lightning", but with that name because it sounds more BIONICLE-esque.
Technically plasma is gas that's electrically charged. In this case he uses this as an electrical method of "fire", using it to inflict heat-based damage, but the gas cannot be as easily controlled to attract or to repel from electrical objects/beings, and cannot cause electric shocks.
He also has a form of "burst lightning", natural lightning created from plasma, which he can use to supercharge an opponent to the point that they explode into plasma.
On the point of earth versus stone, I see stone as hard rocks, and earth as softer dirt, sand, and such.