What exactly is the difference between an interface and abstract class?
Inheritance is used for two purposes:
To allow an object to regard parent-type data members and method implementations as its own.
To allow a reference to an objects of one type to be used by code which expects a reference to supertype object.
In languages/frameworks which support generalized multiple inheritance, there is often little need to classify a type as either being an "interface" or an "abstract class". Popular languages and frameworks, however, will allow a type to regard one other type's data members or method implementations as its own even though they allow a type to be substitutable for an arbitrary number of other types.
Abstract classes may have data members and method implementations, but can only be inherited by classes which don't inherit from any other classes. Interfaces put almost no restrictions on the types which implement them, but cannot include any data members or method implementations.
There are times when it's useful for types to be substitutable for many different things; there are other times when it's useful for objects to regard parent-type data members and method implementations as their own. Making a distinction between interfaces and abstract classes allows each of those abilities to be used in cases where it is most relevant.