Anarchy and order are very much not opposites (There's an O in the logo!), you might be thinking of anomie which means the absence of (legal, social) norms.
From the random yanks I see on the net the dividing line between ancap and libertarian is how open and/or conscious they are about their radicalism, though even ancaps of course fall short of admitting that they're neo-feudalists. Basic differentiating factor from ordinary monarchists is that they want their King (not too uncommonly, it could also be a Queen) to rule by grace of capital instead of god. Which, if you ask Stirner, isn't really much of a distinction both are spooks.