The aftermarket auto warranty, as its name suggests, is a type of warranty that can work on both the new car as well as the used car (aftermarket is generally taken to mean that one fits all).  This is highly unlike any other warranty which is often specific to the type of car it covers – normally only a new car warranty would provide coverage for a new car and a used car warranty would provide coverage to a used car.  It is also known as the extended warranty, particularly because it is used in combination of either of these warranties to extend either the life or the coverage of the existing warranty. 
But in addition to this slight anomaly of the aftermarket auto warranty, we add that the aftermarket auto warranty can be obtained at any dealer or service provider after the vehicle purchase – regardless of when and where the vehicle was purchased.  This may not apply to all however.  The aftermarket auto warranty is like no other warranty because it is the only warranty that you would ever be required to purchase (although sometimes other warranties require a transfer fee to be paid for transfer of the coverage from one owner to another).  In this sense, it is the equivalent of a service contract.  The aftermarket auto warranty is however automatically transferable with the sale of the vehicle so long as it is still valid.