Abstract is object oriented. It offers the basic data an 'object' should have and/or functions it should be able to do. It is concerned with the object's basic characteristics: what it has and what it can do. Hence objects which inherit from the same abstract class share the basic characteristics (generalization).
Interface is functionality oriented. It defines functionalities an object should have. Regardless what object it is, as long as it can do these functionalities, which are defined in the interface, it's fine. It ignores everything else. An object/class can contain several (groups of) functionalities; hence it is possible for a class to implement multiple interfaces.