While I think that anarchism and anarcho-capitalism are two separate ideas, I think they borrow values from the same philosophy, which is ultimately no control. Granted, I would say anarchy is a bit more severe in that respect, since anarcho-capitalism still wants the free market and private companies to elicit some level of control. However, that's hardly "control," since there'd be no system to stop them from abusing their power. Hence the reason it's called "anarcho-capitalism." They're in the same philosophical family, just not identical.
If anarchism is the belief that men need no government because men will find rational means to live together, then anarcho-capitalism is the belief that the main means men will find to resolve their differences will be in the marketplace and through the mechanisms of the marketplace and money, wealth and power.
Anarchism, in general terms, is the freedom from an overruling political body. While there are some distinctions within an anarcho-capitalist system that separate it from similar systems, this basic tenet of anarchism is still adhered to; that is, while the basic belief of anarcho-capitalism is that the influence of the free market will create the stability usually afforded by a state government, that form of governing body would still be absent, and so the system rightly falls within the bounds of anarchism.
Anarchy is a state of lawlessness. Anarcho-capitalism is a state of lawlessness fueled by the need for money. The Old West of American history is a close representation of anarcho-capitalism in real life. Currently, the Mexican border with the United States can also be considered as such since drug cartels rule that area. When money is the norm rather than the law, that's when anarcho-capitalism ensues as money is the law.
The two theories are not the same, really. Any anarcho-capitalist (which isn't even very specific and carries negative connotations) involves an emphasis on self reliance and compromise, while classical anarchism is the furthest extension of left ideology, a step past communism without any sort of central authority or legal system.