Taxis are regulated within an inch of their bright yellow lives, with a big red-tape bow on top. There can be only so many cabs on the streets, and only so many drivers can operate them. Thus the precious medallions, which can sell for as much as $1 million in NYC, that proclaim to the world this car has been approved by a real governmental agency to pick people up and drive them around for a fee.
Uber is neither constrained nor bound to any such regulation. There's no training, though there are now background checks. Uber thinks of itself as an eBay-like tech company in that it merely connects buyers and sellers, but Uber cars obviously pick people up and drive them around in the real world, not the virtual one, just like cabs. This leaves some uncomfortable wiggle room in the liability area when accidents happen and there's no medallion to act as a shield.