What was The difference between the Roman republic and the Greek democracy was that:

One of the most important differences between ancient Greek democracy and ancient Roman Republicanism was institutional. in two ancient Greeks and Roman thinkers conceived of society as containing two permanently distinct and mutually antagonistic group the few (the rich) and the many (the poor). Greek democracy and Roman republicanism dealt with this fact in different ways. For Greek thinkers, democracy was simply the rule of the many over the few, whereas aristocracy or oligarchy was the rule few over the many. Power could only be held by the masses or by the elite.