Can class().method() and class.method() do different things?

Question

I'd like to know if it's possible to have two methods in a class with the same name (or only one if it can do what I want) but the first method would be called on class().method() and the second one on class.method() (example below).

I tried to do it by creating a method with @staticmethod and a second one (with the same name) without.

Here is my example:

class MyClass:
#   @potential_decorator1
    def my_function():
        print("MyClass.my_function() has been called !")

#   @potential_decorator2
    def my_function(self):
        print("Now it's MyClass().my_function() that has been called !")

What I tried:

class MyClass:
    @staticmethod
    def my_function():
        print("MyClass.my_function() has been called !")

    def my_function(self):
        print("Now it's MyClass().my_function() that has been called !")

But when I tested it:

>>> MyClass.my_function()
TypeError: my_function() missing 1 required positional argument: 'self' #I'd like the 
                                                   #staticmethod to be called instead
>>> MyClass().my_function()
Now it's MyClass().my_function() that has been called !

By analyzing it, I understood that the "classic" method overrides the static method.