PRIOR JAVA 8: 

Abstract Class Interfaces
An abstract class can provide complete, default code and/or just the details that have to be overridden. An interface cannot provide any code at all,just the signature.
In case of abstract class, a class may extend only one abstract class. A Class may implement several interfaces.
An abstract class can have non-abstract methods. All methods of an Interface are abstract.
An abstract class can have instance variables. An Interface cannot have instance variables
An abstract class can have any visibility: public, private, protected. An Interface visibility must be public (or) none.
If we add a new method to an abstract class then we have the option of providing default implementation and therefore all the existing code might work properly If we add a new method to an Interface then we have to track down all the implementations of the interface and define implementation for the new method
An abstract class can contain constructors An Interface cannot contain constructors
Abstract classes are fast Interfaces are slow as it requires extra indirection to find corresponding method in the actual clas

JAVA 8: 

Prior to java 8, interface in java can only have abstract methods. All the methods of interfaces are public & abstract by default. Java 8 allows the interfaces to have default and static methods. The reason we have default methods in interfaces is to allow the developers to add new methods to the interfaces without affecting the classes that implements these interfaces.

Static methods in interfaces are similar to the default methods except that we cannot override these methods in the classes that implements these interfaces.

With the introduction of default methods in interfaces, it seems that the abstract classes are same as interface in java 8. However this is not entirely true, even though we can now have concrete methods(methods with body) in interfaces just like abstract class, this doesn’t mean that they are same. There are still few differences between them, one of them is that abstract class can have constructor while in interfaces we can’t have constructors.

The purpose of interface is to provide full abstraction, while the purpose of abstract class is to provide partial abstraction. This still holds true. The interface is like a blueprint for your class, with the introduction of default methods you can simply say that we can add additional features in the interfaces without affecting the end user classes.