return, return None, and no return at all?

Yes, they are all the same.

We can review the interpreted machine code to confirm that that they're all doing the exact same thing.

import dis

def f1():
  print "Hello World"
  return None

def f2():
  print "Hello World"
  return

def f3():
  print "Hello World"

dis.dis(f1)
    4   0 LOAD_CONST    1 ('Hello World')
        3 PRINT_ITEM
        4 PRINT_NEWLINE

    5   5 LOAD_CONST    0 (None)
        8 RETURN_VALUE

dis.dis(f2)
    9   0 LOAD_CONST    1 ('Hello World')
        3 PRINT_ITEM
        4 PRINT_NEWLINE

    10  5 LOAD_CONST    0 (None)
        8 RETURN_VALUE

dis.dis(f3)
    14  0 LOAD_CONST    1 ('Hello World')
        3 PRINT_ITEM
        4 PRINT_NEWLINE            
        5 LOAD_CONST    0 (None)
        8 RETURN_VALUE      

On the actual behavior, there is no difference. They all return None and that's it. However, there is a time and place for all of these. The following instructions are basically how the different methods should be used (or at least how I was taught they should be used), but they are not absolute rules so you can mix them up if you feel necessary to.

Using return None

This tells that the function is indeed meant to return a value for later use, and in this case it returns None. This value None can then be used elsewhere. return None is never used if there are no other possible return values from the function.

In the following example, we return person's mother if the person given is a human. If it's not a human, we return None since the person doesn't have a mother (let's suppose it's not an animal or something).

def get_mother(person):
    if is_human(person):
        return person.mother
    else:
        return None

Using return

This is used for the same reason as break in loops. The return value doesn't matter and you only want to exit the whole function. It's extremely useful in some places, even though you don't need it that often.

We've got 15 prisoners and we know one of them has a knife. We loop through each prisoner one by one to check if they have a knife. If we hit the person with a knife, we can just exit the function because we know there's only one knife and no reason the check rest of the prisoners. If we don't find the prisoner with a knife, we raise an alert. This could be done in many different ways and using return is probably not even the best way, but it's just an example to show how to use return for exiting a function.

def find_prisoner_with_knife(prisoners):
    for prisoner in prisoners:
        if "knife" in prisoner.items:
            prisoner.move_to_inquisition()
            return # no need to check rest of the prisoners nor raise an alert
    raise_alert()

Note: You should never do var = find_prisoner_with_knife(), since the return value is not meant to be caught.

Using no return at all

This will also return None, but that value is not meant to be used or caught. It simply means that the function ended successfully. It's basically the same as return in void functions in languages such as C++ or Java.

In the following example, we set person's mother's name and then the function exits after completing successfully.

def set_mother(person, mother):
    if is_human(person):
        person.mother = mother

Note: You should never do var = set_mother(my_person, my_mother), since the return value is not meant to be caught.