From Driver Rule 54-20 (in PDF): It is against the law to refuse a person based on race, disability, or a destination in New York City. A taxicab driver is required to drive a passenger to any destination in the five boroughs. You can make a refusal complaint by calling 3-1-1.
Hack is short for hackney (from the Middle English hakeney), which at one time described a horse of average size, used for regular riding—as distinct from stronger horses used for hauling or in war. Such horses were often let out for hire to pull a coach or cab.
A taxi, also known as a taxicab or simply a cab, is a type of vehicle for hire with a driver, used by a single passenger or small group of passengers, often for a non-shared ride. A taxicab conveys passengers between locations of their choice.
Officially, taxi is short for taximeter cab, as they were originally named at the turn of the 20th century. Today the taximeter, which records distance and fare, is usually just called a meter.
Uber customers typically get where they are going faster or cheaper than they would by taxis. Partygoers can rely on being able to find available Uber drivers through their apps late at night.