Originally Posted by Brillig

Yes, but not much.

I have a road bike and a hybrid and I still ride the hybrid sometimes when I go riding with my wife. Believe me, there's not that much difference. It's the engine.

Oh, another difference you didn't mention might be pedals, since most hybrids tend to be platform or toe clip and most road bikers tend to use clipless. They actually do make a big difference after you learn to pedal correctly with them.