Capitalism is indeed very different from anarchism. As the horrifying crisis in Russia after the "Big Bang" market reforms shows, capitalism needs a very solid institutional basis to work properly. There is a whole bunch of laws and behaviors that underlie the concept of free competition and without them there are no markets.

Examples:
Property rights: If robbers can take away everything I earn, what's the point in maximising my profits?
Taxpaying: e.g., to pay the policemen to chase the robbers...

And there are many more institutions. The important ones still need to be invented. They are the ones that make sure that capitalism doesn't excessively increase social inequality, and the ones that make sure that priceless things like art and free time will be respected.