Anarchism means something different depending on who one asks. It literally means 'no rulers,' while many emphasize its antagonism to the idea of 'the state.' Some are too lazy when it comes to defining 'state' and others are probably too hard headed when it comes to defining 'rule.' Some anarchists think that power itself shouldn't belong to any one person and are therefore against all hierarchies and all forms of positional leadership. Others simply think that all manners of social organization are permissible insofar as they are not coercive. But then, many people can't seem to agree on just what constitutes coercion. Does one simply remain passive and always wait for the other to strike first or can one do something to preemptively ensure safety? There are yet others who feel, in keeping with Proudhon's maxim, that property itself is theft. Libertarians argue from the opposite direction: that taxation is theft while property is perfectly legitimate.
All this splitting of hairs may offer different economic options for how to organize a society, but economic distinctions alone do not create harmony. No economic or organizational system has ever lasted more than a few hundred years at a time. One has to ask oneself, what is the organizing principle for self determination and self rule if there is one? It is just as difficult to make a natural argument for either authority or freedom, for one can take either variable and treat them exclusively through a materialistic register. But if one looks at them metaphysically, one sees that they're not mutually exclusive but exist in degrees due to both their imminent characteristics and relationship with the world around them.
Freedom sounds nice, but what exactly is it? If you let a child free in the forest, it isn't going to do well. It will be limited by its lack of experience and lack of developed motor skills. We are all limited in our self determination and free in our self determination, to varying degrees and in varying ways. Some are more skilled and equipped to deal with certain information and tasks. Some in this position have become kings. Others have become shrewd business men, creating a service and thus, providing a demand. But then, not everyone wants to be a peasant or a customer.
Of course, these aren't the only options. As stated before, everyone is free to the degree that they are unbound by certain restrictions do to personal agency, though absolutely everyone has limited agency to some degree.
An anarchist is, at the end of the day, a passive category. Not only does it assert a unilateral principle of 'no rulers' which is contradicted by many basic societal transactions, but it is a position that usually desires the same position for everyone else; even those whose agency is limited. While simple on the surface, it is a position in isolation of the current world order, in that there is nowhere that one can escape to that is not technically governed.
Most anarchists reading this would probably say, 'So you justify government because someone is going to rule anyway?' On the contrary, I argue only that this would have to be the final conclusion of a passive position if you took it to its farthest conclusion. Most free, anarchic zones throughout history have been knocked over by some sort of dictatorship. Dictatorship is, you might say, an advancement of the passive anarchist view, in that one man's escape from all rule creates a sort of black hole, into which all must satiate his unbending will or suffer whatever measures the dictator needs to protect whatever he has acquired for himself in his journey toward total freedom.
Autarchy, on the other hand, is an active position. It remains active precisely because it doesn't limit itself to the economic domain. It is more of an ontological distinction. Autarchy, rather, means 'self rule.'
But what does it mean to rule oneself? It not only implies ownership of one's body, but a mastery of the inner domain; of one's fleeting passions and passive traits. One might say this is all good and well as a philosophical distinction, but what does it do for someone living in a particular, modern political and economic climate? Autarchy could then best be seen as an underlying principle; a standard that a group of people are trying to apply to themselves in one environment. If you strengthen the principles on which a form of social organization are founded, they'll manifest through the economy and through various day to day transactions. Principles of autarchy may, if fully realized, lead to an organic sort of anarchic society, or simply an autonomous society, if you prefer that term.
But in truth, there is always going to be someone who is better at things than you are. In some instances, this is going to manifest in a form of monetization; through the free market. In some cases, however, one person might be better at many things everyone else in the community is not. This is a kind of power, but it is not necessarily a coercive power. It is a position in which others are likely to follow another's leadership naturally. Those who lead best (which is, again, not the same as ruling through fear of sheer might) are often people who have learned how best to rule themselves and act as examples as to how others should better themselves as well.
Think about certain heroes you might have, whether artists or religious leaders or people you know. If you don't like what they have to offer, you simply tune out. By doing this, you naturally become excluded from whatever process they happen to keep functioning. This is far less coercive than large, statist government and is how most of society runs anyway. It just elevates the role of personal responsibility in society. In this society, everyone is both led and leads to some degree. As a principle, it is a balancing act of strength and humility.
I'm no romantic on this subject, however. I don't think that we can just evolve toward this point or start teaching it in our institutions, or enstating laws which require you to follow these guidelines. It is something one has to exercise in one's daily life and offer to others by way of transmission and inspiration. But when you're truly living your life according to this kind of principle, you are more than likely going to find other people on the same path. It is a state of being more than a way of organizing a state (or non-state). If it is achieved, however, there is almost nothing that couldn't be done.