Technically, Equestria isn't a monarchy. It's a diarchy as Celestia and Luna rule as equals. Also a principality can be a monarchical (or diarchical in this case) state. It simply means the title of the ruler(s) is prince or princess. Another difference between a kingdom and a principality would be relative size of territory (with a kingdom being bigger). Also in diplomatic functions, like a large banquet, noble rank determines who sits where, who defers to whom, forms of address, and all that fancy stuff.