Very simply, “anarchy” is descriptive of a human being, or humanity, that lives without hierarchy (social control & power). A way of life most conducive to choices on behalf of life itself. Beyond that, I don't believe it could really be said to have any crystalline character to what it is or could be.
Anarchism is a distinct array of political ideas, ideologies, literature, and just generally intellectual or practical pursuits composed by a diverse milieu, as well as tradition, of people who oppose hierarchy *on principle* and have largely given themselves the task of expounding, illustrating, as well as demonstrating the values (namely anarchy) that result from those principles. Anarchism exists in a world where it is truly unwelcome and this divorces anarchism from even the horizon of anything like a way of life it envisions itself as belonging to. And so anarchism is also definitely a conceit which often betrays itself as such.
In the interest of relating the site's content back to itself I'll refer to another answer given to a similar question:
“Anarchism is as a political philosophy that aspires to a world without the State and without exchange relations [relations dominated by the market and economic value]. It is both the negative idea that there is a laundry list of ideas, practices, and values in our current society to be against and the positive idea that what is most "us" about us (as living creatures) should be free to pursue its own ends without coercion or constraint.
Anarchism is also a variable. It means many different things to different people. This open nature to the term serves as a counter-point to ideas that are connected to specific thinkers or traditions in that, while there is a tradition, and there are important thinkers, there is also a lot of room for -you- to write your own page to the story. To apply the variable to your own life.
Anarchism is also a constraint. For many, if not most, anarchists there is a central concept that the ends do -not- justify the means, or put more gently, that an anarchist practice must embed the values and ideas of a future anarchist society. This means that anarchists are often broken into parts. One part acts against the constraints of this world. The other part constrains themselves by an ethical ruler the calibration of which is in a foreign unit.”
