Well shit
<Snipped quote by Buddha>
Not quite.
Anarchists believe that systems of authority are more or less illegitimate and unnecessary, and that if you got rid of them society would not only still function, but it would function better because the suppressive nature of force wouldn't be keeping the population from realizing it's full potential. It isn't like "If we get rid of parents we can have a wild party", it's "The guys making the rules are just bending everything for their own benefit at the expense of society, if we get rid of them and make the rules ourselves we can actually make them work."
Anarchism is more like super-democracy, still requiring rules but putting them in the hands of the masses rather than selected (or self appointed) con artists. You can say you think that would cause random chaos, but that's not the same thing as saying anarchists are for random chaos.
An-Caps believe basically the same thing, but just about government. So an an-cap believes that all governing bodies are illegitimate, but private capital is completely separate from government and should be maintained by common consent and private security. They are totally fine with the anarchist system of super-democracy, they just don't want it to touch private capital.