Democracy - The ability to vote peridically and demonstrate , the constitution are all various institutions that give power to citizens to influence the decisions of the ruler.
Capitalism - a combination of cooperation and competition by companies to achieve goals many consumers cooperate on getting(by paying). BTW when a few companies compete on the same goal , it's also a kind of cooperation.
Not to split hairs, but that would be "free markets".
Free markets are neither necessary nor sufficient condition for capitalism. Compare the US in its heyday vs. the present day "state capitalism" in Europe and China.
