Uber is deliberately blurring the lines by offering "Uber Taxi" alongside the black car service; they are putting themselves directly into competition with regulated cab services. Uber Taxi isn't intended to be a market substitute for cab service; it's intended as a replacement for cab service.

Incidentally, the "on-demand" nature of taxicabs versus the "call-ahead" nature of car services is not a distinction made in every city or state. Arlington's "taxi cab" definition pretty clearly captures car services as well.