anarchism is the fundamental and unbending belief in the libertarian principle of non-aggression; that no one has the right to aggress against the person or property others, summed up in the NAP.
there are various divisions of anarchism based on subjective ideological preferences, the big three being anarcho-syndicalism, anarcho-capitalism and anarcho-communism. these ideologies differ from the state versions in the fact that none of them wish to impose such ideologies upon others, but to voluntarily associate.
all of these, however, fit under common headings. all anarchists are market anarchists. all market anarchists are libertarians. being that the NAP is the basis for libertarianism, anarchism must fit beneath that heading because no true anarchist can support the rule of one over others. all anarchism must fall beneath the heading of market anarchism because, in order for conditions to be conducive to people engaging in voluntary socio-economic arrangements, there can be no restrictions on markets, which facilitate free exchange and cooperation in whatever form, not to mention that there must be rule over others in order to eliminate markets.
a diagram explaining the above paragraph:
in the condition of free markets, all are able to decide which arrangements they prefer whether they be communists, syndicalists, capitalists or any combination of the three or something else entirely. often, the collectivist anarchists (communists and syndicalists) will deny the need for a free market in an anarchist society, but it usually stems from an incomplete understanding of markets and a general tendency to conflate free markets and capitalism. admittedly, capitalism tends to flourish under free markets, but it need not exist at all for free markets to exist.
i admit to being an advocate of capitalism. it is the best way to provide the highest quality of life (measured in traditional terms) for the most people given limited resources. that said, my allegiance to capitalism is thin. it is merely a practical support, not an ideological one. if the markets were to determine that society be composed of various communes without a representative constituency of capitalists, i would gladly accept communism and be happy to live free.
as should be the case with any true anarchist, one's anarchism should come first and all other ideological considerations should be secondary.