The main reason for using abstract classes and interfaces are different.
An abstract class should be used when you have classes that have identical implementations for a bunch of methods, but vary in a few.
This may be a bad example, but the most obvious use of abstract classes in the Java framework is within the java.io classes.  OutputStream is just a stream of bytes.  Where that stream goes to depends entirely on which subclass of OutputStream you're using... FileOutputStream, PipedOutputStream, the output stream created from a java.net.Socket's getOutputStream method...
Note: java.io also uses the Decorator pattern to wrap streams in other streams/readers/writers.
An interface should be used when you just want to guarantee that a class implements a set of methods, but you don't care how.
The most obvious use of interfaces is within the Collections framework.
I don't care how a List adds/removes elements, so long as I can call add(something) and get(0) to put and get elements.  It may use an array (ArrayList, CopyOnWriteArrayList), linked list (LinkedList), etc...
The other advantage in using interfaces is that a class may implement more than one.  LinkedList is an implementation of both List and Deque.