What are the differences between a `classmethod` and a metaclass method?

When you phrase it like you did in the question, the @classmethod and metaclasses may look similar but they have rather different purposes. The class that is injected in the @classmethod's argument is usually used for constructing an instance (i.e. an alternative constructor). On the other hand, the metaclasses are usually used to modify the class itself (e.g. like what Django does with its models DSL).

That is not to say that you can't modify the class inside a classmethod. But then the question becomes why didn't you define the class in the way you want to modify it in the first place? If not, it might suggest a refactor to use multiple classes.

Let's expand the first example a bit.

class C:
    @classmethod
    def f(cls):
        print(f'f called with cls={cls}')

Borrowing from the Python docs, the above will expand to something like the following:

class ClassMethod(object):
    "Emulate PyClassMethod_Type() in Objects/funcobject.c"

    def __init__(self, f):
        self.f = f

    def __get__(self, obj, klass=None):
        if klass is None:
            klass = type(obj)
        def newfunc(*args):
            return self.f(klass, *args)
        return newfunc

class C:
    def f(cls):
        print(f'f called with cls={cls}')
    f = ClassMethod(f)

Note how __get__ can take either an instance or the class (or both), and thus you can do both C.f and C().f. This is unlike the metaclass example you give which will throw an AttributeError for C().f.

Moreover, in the metaclass example, f does not exist in C.__dict__. When looking up the attribute f with C.f, the interpreter looks at C.__dict__ and then after failing to find, looks at type(C).__dict__ (which is M.__dict__). This may matter if you want the flexibility to override f in C, although I doubt this will ever be of practical use.

As classes are instances of a metaclass, it is not unexpected that an "instance method" on the metaclass will behave like a classmethod.

However, yes, there are differences - and some of them are more than semantic:

1. The most important difference is that a method in the metaclass is not "visible" from a class instance. That happens because the attribute lookup in Python (in a simplified way - descriptors may take precedence) search for an attribute in the instance - if it is not present in the instance, Python then looks in that instance's class, and then the search continues on the superclasses of the class, but not on the classes of the class. The Python stdlib make use of this feature in the abc.ABCMeta.register method. That feature can be used for good, as methods related with the class themselves are free to be re-used as instance attributes without any conflict (but a method would still conflict).
2. Another difference, though obvious, is that a method declared in the metaclass can be available in several classes, not otherwise related - if you have different class hierarchies, not related at all in what they deal with, but want some common functionality for all classes, you'd have to come up with a mixin class, that would have to be included as base in both hierarchies (say for including all classes in an application registry). (NB. the mixin may sometimes be a better call than a metaclass)
3. A classmethod is a specialized "classmethod" object, while a method in the metaclass is an ordinary function.

So, it happens that the mechanism that classmethods use is the "descriptor protocol". While normal functions feature a __get__ method that will insert the self argument when they are retrieved from an instance, and leave that argument empty when retrieved from a class, a classmethod object have a different __get__, that will insert the class itself (the "owner") as the first parameter in both situations.

This makes no practical differences most of the time, but if you want access to the method as a function, for purposes of adding dynamically adding decorator to it, or any other, for a method in the metaclass meta.method retrieves the function, ready to be used, while you have to use cls.my_classmethod.__func__ to retrieve it from a classmethod (and then you have to create another classmethod object and assign it back, if you do some wrapping).

Basically, these are the 2 examples:

class M1(type):
    def clsmethod1(cls):
        pass

class CLS1(metaclass=M1):
    pass

def runtime_wrap(cls, method_name, wrapper):
    mcls = type(cls)
    setattr(mcls, method_name,  wrapper(getatttr(mcls, method_name)))

def wrapper(classmethod):
    def new_method(cls):
        print("wrapper called")
        return classmethod(cls)
    return new_method

runtime_wrap(cls1, "clsmethod1", wrapper)

class CLS2:
    @classmethod
    def classmethod2(cls):
        pass

 def runtime_wrap2(cls, method_name, wrapper):
    setattr(cls, method_name,  classmethod(
                wrapper(getatttr(cls, method_name).__func__)
        )
    )

runtime_wrap2(cls1, "clsmethod1", wrapper)

In other words: apart from the important difference that a method defined in the metaclass is visible from the instance and a classmethod object do not, the other differences, at runtime will seem obscure and meaningless - but that happens because the language does not need to go out of its way with special rules for classmethods: Both ways of declaring a classmethod are possible, as a consequence from the language design - one, for the fact that a class is itself an object, and another, as a possibility among many, of the use of the descriptor protocol which allows one to specialize attribute access in an instance and in a class:

The classmethod builtin is defined in native code, but it could just be coded in pure python and would work in the exact same way. The 5 line class bellow can be used as a classmethod decorator with no runtime differences to the built-in @classmethod" at all (though distinguishable through introspection such as calls toisinstance, and evenrepr` of course):

class myclassmethod:
    def __init__(self, func):
        self.__func__ = func
    def __get__(self, instance, owner):
        return lambda *args, **kw: self.__func__(owner, *args, **kw)

And, beyond methods, it is interesting to keep in mind that specialized attributes such as a @property on the metaclass will work as specialized class attributes, just the same, with no surprising behavior at all.