The term “taxicab” includes any motor vehicle operated upon any street or highway or on call or demand accepting or soliciting passengers indiscriminately for transportation for hire between such points along streets or highways as may be directed by the passenger or passengers being transported, provided nothing in this chapter shall be construed to include, as a taxicab, a motor bus, as defined in section 14-1, a motor vehicle in livery service when such motor vehicle is hired for a specific trip or trips and is subject to the direction of the person hiring the same, or a transportation network company vehicle, as defined in section 13b-116.