Classical and prototype-based inheritance are two different approaches to implementing inheritance in object-oriented programming. The key differences between these two approaches are:

1. Class-based vs. Object-based: In classical inheritance, you define a class, which is a blueprint for creating objects. Objects are then created by instantiating the class. In contrast, in prototype-based inheritance, there are no classes. Objects are created directly from other objects, and inheritance is achieved by copying properties and methods from one object to another.

2. Inheritance Hierarchy: In classical inheritance, there is a clear hierarchy of classes, with each class inheriting from a single parent class. This creates a tree-like structure, with the root being the base class. In contrast, in prototype-based inheritance, there is a network of objects that can inherit from multiple objects at the same time, creating a more complex structure.

3. Overriding: In classical inheritance, you can override methods and properties in a subclass, effectively replacing them with new implementations. In prototype-based inheritance, you can also override properties and methods, but it is more difficult to completely replace them, since objects inherit properties and methods from multiple sources.

4. Dynamic vs. Static: In prototype-based inheritance, objects can be modified at runtime, since they are not tied to a class definition. In classical inheritance, the structure of the class hierarchy is fixed at compile time, and objects cannot be modified dynamically.

5. Syntax: In classical inheritance, you define classes using a specific syntax, and then create objects using the new keyword. In prototype-based inheritance, you create objects directly using an object literal or the Object.create() method.

Both classical and prototype-based inheritance have their advantages and disadvantages, and the choice of which approach to use depends on the specific needs of the application and the programming language being used.