Inheritance - Need Both Scripts Attached?

Hello,

Sorry if this is a silly question. When designing a class that inherits from another class, I'm wondering if the base script (parent class) has to be attached to the same object as the child class? Or can you just attach the child class to the object without the parent?

For example, if I were making a Pokemon card game, and I had a parent class called "Card," and then a child that references Card called Pikachu, would I have to attach both scripts to the object, or just Pikachu?

Thanks!