What's the difference and why does it matter?
In a democracy the community of people hold power over how they are governed (All eligible citizens get equal day in decisions). In a republic decisions are made via elected representatives.
There's nothing inherently wrong with a republic but clearly we can see things CAN become massively corrupted by greed, power and influence. This leads to our current atmosphere where policy is passed opposite to the public majority.
In a true democracy the people would be voting on everything, which would take a massive effort of time and resources. Although, what would this look like in a modern day society? Perhaps a government website where you log in via your social security number and vote on policy when you see fit.
I don't have a solution or point to this but I just wanted to remind everyone that America preaches democracy and fairness, yet we don't even govern ourselves that way!