Here is a good discussion of these differences: http://www.lexrex.com/enlightened/AmericanIdeal/aspects/demr...
Why do we need so many middlemen? Is this _really_ a democracy? Or is it a mere visibility of "rule of the people" designed to keep the working class, well, working, for the benefit of the ruling class?
For some reason you are arguing as if a direct democracy would somehow magically address the problems you outline for a representative democracy.
But in all but the smallest organizations, a direct democracy is simply unworkable and so your complaints don't really move the discussion forward. Do you want to go to the ballot box once a week to vote on every decision currently made by your representatives at the local, state, and federal level? Do you think that is more workable than a representative mechanism?
Actually, it most often representative democracy, which may be a republic, but may just as easily be, say, a constitutional monarchy.