Here are some differences: Direct Democracies of history have no constitution to speak of, no protection for rights, do not give equal rights to all citizens (no rights for minorities, women had no rights in Greece), do not have full representation, no checks and balances (people were judge, leglislature and executive all in one), and they had no basis for right and wrong other than the whim of the majority who vote themselves all of the favors and rights. No princple of self governance. No differences huh? History begs to differ with you. Our Christian founding fathers recognized that men are evil, whether they be kings or the people. Separation of powers was devised to protect against the corrupting rule of power-hungry leaders (read Montesquieu - that is where they got this idea); Electoral college, Bill of Rights, federalism were all devised to protect against the corrupt rule of the majority. No differences huh? It seems there are major differences and many of them. Don't you get tired of being wrong?
You're the first one to mention a direct democracy. There's a word for that, but it escapes me right now. A democracy may or may not have a constitution, same as a republic. You're equating democracy with mob rule. Time to go back to a real school (where did you go to school again?)