Why does object's type refer to its interface?

Why does object's type refer to its interface? Why the term type is used here? In terms of C++ I am not able to understand it.

Gamma, Erich. Design Patterns: Elements of Reusable Object-Oriented Software (Addison-Wesley Professional Computing Series) (Kindle Locations 593-596). Pearson Education. Kindle Edition.

An object’s class defines how the object is implemented. The class defines the object’s internal state and the implementation of its operations. In contrast, an object’s type only refers to its interface—the set of requests to which it can respond. An object can have many types, and objects of different classes can have the same type.