API-----A set of routines that an application uses to request and carry out lower-level services performed by a computer's operating system. Also, a set of calling conventions in programming that define how a service is invoked through the application

DLL----A DLL (Dynamic Link Library) is a file that can be loaded and executed by programs dynamically. Basically it's an external code repository for programs. Since usually several different programs reuse the same DLL instead of having that code in their own file, this dramatically reduces required storage space. A synonym for a DLL would be library