Anarchism vs. anarchy
I think it’s important to take a moment to make this distinction. Anarchism is a well-thought-out revolution leading to a well-thought-out lifestyle, free of oppressive/coercive hierarchies. It is an implementation of true freedom that leads to peaceful co-existence and cooperation.
Anarchy is an implementation of true freedom without any other facets. Lacking the thoughtfulness and cooperative/voluntary structures of anarchism, it is a moment of chaos which occurs when hierarchies crumble and there are non-anarchists present.
I say non-anarchists but what I really mean are people ill-equipped, mentally and intellectually, to think for themselves in all aspects of life without an authoritarian structure in place to think for them. Faced with the sudden loss of that authoritarian structure, these people are prone to descend into chaos until either someone educates them, someone imposes a new authoritarian structure upon them, or the unsustainability of chaos catches up with them.
Anarchy unfortunately has a tendency to welcome new authoritarian structures, as many of those people will be seeking new structures to think for them at the same time as their own behavior is erratic and their lifestyles are unsustainable.
What anarchism promises is a non-authoritarian structure that can be put in place, or even transitioned into, to avoid anarchy and the chaos which accompanies it. It’s about sustainable structures which withstand the test of time. Finally, it’s about enabling the people – both mentally and physically – to prohibit and crush any authoritarian uprisings that may seek to once more oppress them, rather than going on to seek out such structures and willingly submit to them.

8:13 pm
I’d say this is a pretty strange use of terminology. Anarchism is a political idea; anarchy is a state. They are in different domains, and cannot be compared.
Of course it’s true that the collapse of a government is a chaotic sort of anarchy — probably the chaos caused the government to collapse in the first place, and in that kind of situation, the lack of a government certainly isn’t going to help.
However, societies that predate governments also exist(ed) in a state of anarchy, and that was not so chaotic. They weren’t anarchists, since they didn’t have a government to abolish — they had no need for the political idea of anarchism. But they had anarchy, and yet their societies were ordered and stable, and relative to statist societies, very much egalitarian.