Uber and Lyft call themselves "ridesharing" programs where passengers "donate" money to a driver who "just happens" to be going to the same destination as his passengers but who will not remain at that destination and who will probably pick up more passengers shortly thereafter and "coincidentally" drive them to their desired location in exchange for a "donation." Uber and Lyft can use all the euphemisms they want, but they what they are is the very definition of a for-hire car service.
The fact that they straddle the line between two types of regulated car services (cabs and limos/"charter car") does not change the essence of the commercial transaction that takes place. The fact that a mobile app or website is used to arrange the transaction instead of a phone call does not change the essence of the commercial transaction that takes place.
Regulations on cars-for-hire exist for a reason: to protect the safety of passengers by ensuring a minimal level of competence and to ensure recompense via adequate capital or insurance in the event of an accident. These regulations work remarkably well, which is why so many people think they are unnecessary.