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.