Factory Method Design Pattern -PHP

I am reading about factory design pattern, this pattern comes in 3 forms, simple factory, factory method and abstract factory.

what I understand, that's simple factory is not a design pattern, it just a type of encapsulate the object creation code in conjunction with if/switch statement or direct loading for the classes with exception if the class not exist!.

When I tried to move to factory method I can't find a clear enough example to defer it from simple factory.

could you guys give an example that's explain the factory method and how its defer from simple factory?

Thank you.