The different between a representative democracy and a direct democracy?

Direct democracy means every citizen gets to vote and has a say in the government. Representative democracy means we vote on officials to represent us and make decisions for us.
The difference between them is how much suffrage's/sufferance taxpayers are willing to forgive to the few given charge of their authority who then would have power to rule? To police? To spend? To choose our enemies?
To be our trusted servant's? How is that "by our our vote" ~ without duty ^ a just trust us contract?
Do they get policed? What if they become a Kleptocracy?
Does that mean they can judge us for our own good too?
Off the top of my head isn't this like fourth century BC. Rome when/how the representation of the public "republic" came to power (senate) or is that the Imperial prelate~ magistrate of the monarchy the military branch of law we call substantive Pontiff Pilate expressed as the spirit of judicial authority (under due process today) to side with the natural or supernatural law of the land?
As elaborate as can be the point in history where time began man began to govern with Gods authority and its clearly not about being holy it is about superiority over the common minded by the Masters of us, of having our permission to have the last word in judgment!