Difference between foo.bar() and bar(foo)?

In terms of just calling the method, there is no difference most of the time. In terms of how the underlying machinery, works, there is a bit of a difference.

Since show_info is a method, it is a descriptor in the class. That means that when you access it through an instance in which it is not shadowed by another attribute, the . operator calls __get__ on the descriptor to create a bound method for that instance. A bound method is basically a closure that passes in the self parameter for you before any of the other arguments you supply. You can see the binding happen like this:

>>> billy_cyrus.show_info
<bound method Parent.show_info of <__main__.Parent object at 0x7f7598b14be0>>

A different closure is created every time you use the . operator on a class method.

If you access the method through the class object, on the other hand, it does not get bound. The method is a descriptor, which is just a regular attribute of the class:

>>> Parent.show_info
<function __main__.Parent.show_info>

You can simulate the exact behavior of binding a method before calling it by calling its __get__ yourself:

>>> bound_meth = Parent.show_info.__get__(billy_cyrus, type(billy_cyrus))
>>> bound_meth
<bound method Parent.show_info of <__main__.Parent object at 0x7f7598b14be0>>

Again, this will not make any difference to you in 99.99% of cases, since functionally bound_meth() and Parent.bound_meth(billy_cyrus) end up calling the same underlying function object with the same parameters.

Where it matters

There are a couple of places where it matters how you call a class method. One common use case is when you override a method, but want to use the definition provided in the parent class. For example, say I have a class that I made "immutable" by overriding __setattr__. I can still set attributes on the instance, as in the __init__ method shown below:

class Test:
    def __init__(self, a):
        object.__setattr__(self, 'a', a)
    def __setattr__(self, name, value):
        raise ValueError('I am immutable!')

If I tried to do a normal call to __setattr__ in __init__ by doing self.a = a, a ValueError would be raised every time. But by using object.__setattr__, I can bypass this limitation. Alternatively, I could do super().__setattr__('a', a) for the same effect, or self.__dict__['a'] = a for a very similar one.

@Silvio Mayolo's answer has another good example, where you would deliberately want to use the class method as a function that could be applied to many objects.

Another place it matters (although not in terms of calling methods), is when you use other common descriptors like property. Unlike methods, properties are data-descriptors. This means that they define a __set__ method (and optionally __delete__) in addition to __get__. A property creates a virtual attribute whose getter and setter are arbitrarily complex functions instead of just simple assignments. To properly use a property, you have to do it through the instance. For example:

class PropDemo:
    def __init__(self, x=0):
        self.x = x
    @property
    def x(self):
        return self.__dict__['x']
    @x.setter
    def x(self, value):
        if value < 0:
            raise ValueError('Not negatives, please!')
        self.__dict__['x'] = value

Now you can do something like

>>> inst = PropDemo()
>>> inst.x
0
>>> inst.x = 3
>>> inst.x
3

If you try to access the property through the class, you can get the underlying descriptor object since it will be an unbound attribute:

>>> PropDemo.x
<property at 0x7f7598af00e8>

On a side note, hiding attributes with the same name as a property in __dict__ is a neat trick that works because data descriptors in a class __dict__ trump entries in the instance __dict__, even though instance __dict__ entries trump non-data-descriptors in a class.

Where it can Get Weird

You can override a class method with an instance method in Python. That would mean that type(foo).bar(foo) and foo.bar() don't call the same underlying function at all. This is irrelevant for magic methods because they always use the former invocation, but it can make a big difference for normal method calls.

There are a few ways to override a method on an instance. The one I find most intuitive is to set the instance attribute to a bound method. Here is an example of a modified billy_cyrus, assuming the definition of Parent in the original question:

def alt_show_info(self):
    print('Another version of', self)

billy_cyrus.show_info = alt_show_info.__get__(billy_cyrus, Parent)

In this case, calling the method on the instance vs the class would have completely different results. This only works because methods are non-data descriptors by the way. If they were data descriptors (with a __set__ method), the assignment billy_cyrus.show_info = alt_show_info.__get__(billy_cyrus, Parent) would not override anything but would instead just redirect to __set__, and manually setting it in b billy_cyrus's __dict__ would just get it ignored, as happens with a property.

Additional Resources

Here are a couple of resources on descriptors:

• Python Reference - Descriptor Protocol: http://python-reference.readthedocs.io/en/latest/docs/dunderdsc/
• (Official?) Descriptor HowTo Guide: https://docs.python.org/3/howto/descriptor.html