In more general terms, the 'porcelain' is the user-friendly interface commands, and the 'plumbing' is the internal commands.
With Git, it's often said that some of the 'porcelain' commands only make sense in the context of the 'plumbing' ones, and you should understand the internals first before being able to use the more user-friendly interface. It's things like this that lead people to create more friendly interfaces like Legit here.
