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I found those two terms in the book of Meyers, but what is the difference?
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Interface inheritance is public inheritance, while implementation inheritance is private inheritance. If class B publicly inherits from A, B is an A: it inherits the whole interface of A, and a (reference/pointer to) a B object can be automatically be upcasted to A, and used wherever an object of A is expected.
a Interface declares the methods and fields and if a class implements that interace it must have all methods and fields of that interface. interface is the one which contains oly the abstract methods, and the class which contains methods which gives the definition to those abstract methods are implementation.
Implementation inheritance is the mechanism whereby a subclass re-uses code in a base class. By default the subclass retains all of the operations of the base class, but the subclass may override some or all operations, replacing the base-class implementation with its own.
Interface inheritance and interface implementation are not the same thing. A class implements an interface by declaring that it implements an interface and then containing the required members to to implement that interface. Interface inheritance refers to an interface inheriting from one or more other interfaces.
Interface inheritance is public inheritance, while implementation inheritance is private inheritance.
If class B publicly inherits from A, B is an A: it inherits the whole interface of A, and a (reference/pointer to) a B object can be automatically be upcasted to A, and used wherever an object of A is expected. However, if B privately inherits from A, B is-implemented-in-terms-of A: only the implementation of A is inherited, not its interface. Thus (references/pointers to) B objects can not be used in places where A objects are expected.
To reflect on @Michal's comment, here are some links (based largely on googling "c++ implementation inheritance") to demonstrate the common usage of these terms in the context of C++:
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Implementation (or class) inheritance is when you separate a common part of implementation in the base class.
Interface inheritance is when you use virtual methods. It is intended to separate interface from implementation and minimize dependencies between program elements.
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The major difference is interface is public inheritance and implementation is private inheritance. The data members and method of the public and protected section will be inherited from base class to derived class in their respective access specifier in public inheritance.At the same time the object of derived class can access the data members of base class as the normal method. The data members and methods of public and protected section will be inherited from base class to derived class in private access specifier
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