The 10g stranded is both bulkier because of the strands and also because of how it's expected to be used there is a lot more/more complicated insulation to keep it from overheating. You need the standard though for anything where you move the wire around because the solid will work harden and break.
The"neutral" is the return path for 120v. For 240v the two hot wires are out of phase so the difference between the peaks is twice as high as the difference between one of them and the ground/neutral (thus 240 vs 120).
The ground wire is the emergency return path. For 240v you don't need a neutral because you're using the delta between the hours but you do need the emergency return path in case some voltage leaks to the components. For 120v, same basic idea. The idea is to present a "shorter" path to any electrical faults than the user provides. Most of the electrical safety mojo is to help keep the user from being the shortest path.
Love thy neighbor, yet pull down not thy hedge.