What is an interface class and what is an abstract class?

The term interface class does not exist in C#. If this is a term describing a class being an interface to other component (human, subsystems, etc), it is very application specific. The designer of that application should know the abstraction.

However, C# does have another type called interface. An interface is NOT a class. An interface defines the intention of some behaviors that classes may be extended it and provides the implementation. The intention, is nothing but method signatures, which defines the return data type, the method name, and any method arguments and associated data type. The implementation is the code of the method. Interface is used for separating the concern of design and implementation.

Abstract class is a class with abstract keyWord. It can be just like a class without that keyWord (then, why it is an abstract class?). But it may have some methods or properties defined as abstract. These abstract methods, like the method signatures of an interface, defines the intention.

The subclasses of such an abstract class would need to implement those abstract methods (providing the code).

There are more common, differences between interfaces and abstract classes, please see answer(s) of those related questions in C# category.