The most interesting part of this question is its mere existence. That a religion of economics upon which so many people hitch their wagon, still struggles to come up with uniform and generally understood definitions of its pivotal suppositions. Exactly the reason why economics must be reinvented to become a viable operating-system for mankind.
Capitalism is nothing more than the exchange of money for products or services rendered. And thus is omnipresent in all classifications of societies imaginable.
I yield to Noam for his best rendition of his thoughts on the subject.