How do you figure? Uber Black is their high end service: professional drivers in luxury cars. The cost is 2-3 times that of Uber X, and (depending on your city) can be more expensive than a cab.
Private black car service means Jeaves is waiting for you in an S Class anywhere you go in the world. Uber Black is basically just higher tier Uber, they don't sit outside idle waiting for you to finish your meetings though, they're just an app way to hail an airport cab. Again, big difference.