Why does class inheritance and interface implementation involve objects?

It's also important to understand the difference between class inheritance and interface inheritance (or subtyping). Class inheritance defines an object's implementation in terms of another object's implementation. In short, it's a mechanism for code and representation sharing. In contrast, interface inheritance (or subtyping) describes when an object can be used in place of another.
_{---《Design Patterns: Elements of Reusable Object-Oriented Software 1st Edition》}

1. Inheritance, isn't it simply about subclasses 'inheriting' properties and methods from the parent class. How does it become 'an object's implementation in terms of another object's implementation'? When I implement class B inheriting from class A in my code, I don't instantiate any objects at all!

2. Isn't an interface just a special kind of abstract class? (In comparison to abstract classes, interfaces only declare methods and don't declare properties or fields.) When a concrete class implements an interface, isn't it simply a class inheriting the 'interface' and implementing the methods declared in the interface? How does this turn into 'an object can be used in place of another'? When I make class B implement interface A in my code, I don't instantiate any objects at all!