Sorry, Uber is a cab company, no matter what they say.
I'm not a fan of Uber but I'm not certain this is true, in my understanding a typical cab will drive around looking for random people to wave it down and potentially wait at certain high pickup locations.
An Uber (or Lyft) vehicle will only respond to a request from the webapp, it strikes me as more analogous to a Limo service or other hired vehicle. Are those considered taxis? (not rhetorical, I'm actually curious. For tax purposes it appears they are).
I live in a city in the Midwest, and have traveled for work to many other cities in the Midwest. Nigh universally, there is no such thing as a taxi that drives around looking for fares. You call a taxi company, or use their website, to request a taxi be dispatched to your location.
Rarely, in some cities, there are designated areas called "taxi stands" located in or near neighborhoods with a high density of bars. Taxis can sometimes be found idling there, waiting for inebriated folks to stumble their way. This is far from a ubiquitous practice, and even where the taxi stands exist, generally only contain taxis on Friday and Saturday nights.
Perhaps taxis continually circle or wait around high-traffic locations in very large cities. However, even on my trips to Chicago, I've seen only the dispatch request model.