Anarchy red on black flag
Anarchy, has more than one colloquial definition. In the United States, the term "anarchy" typically is meant to refer to a society which lacks publicly recognized government or violently enforced political authority. When used in this sense, anarchy may or may not be intended to imply political disorder or lawlessness within a society.
Outside of the US, and by most individuals that self-identify as anarchists, it implies a system of governance, mostly theoretical at a nation state level although there are a few successful historical examples, that goes to lengths to avoid the use of coercion, violence, force and authority, while still producing a productive and desirable society.