What's the difference between an instance method, a classmethod, and a staticmethod?

The three method types side by side

class Pizza:
    def __init__(self, toppings):
        self.toppings = toppings

    def add_topping(self, topping):        # instance method: needs a specific pizza
        self.toppings.append(topping)

    @classmethod
    def margherita(cls):                    # classmethod: alternative constructor
        return cls(["mozzarella", "tomato"])

    @staticmethod
    def is_valid_topping(name):             # staticmethod: no self/cls needed
        return name.lower() in KNOWN_TOPPINGS

• add_topping needs self because it mutates a specific pizza's toppings — calling it makes no sense without an instance.
• margherita is a factory method: Pizza.margherita() builds a new instance without the caller needing to know the constructor's exact argument list. cls refers to the actual class it's called on, so a subclass calling margherita() correctly builds that subclass, not hard-coded to Pizza.
• is_valid_topping doesn't touch instance or class state at all. It's grouped inside Pizza purely for namespacing/discoverability (Pizza.is_valid_topping("basil")), and could just as well be a module-level function.

Why classmethod respects subclassing and staticmethod doesn't apply

class StuffedCrustPizza(Pizza):
    pass

StuffedCrustPizza.margherita()   # returns a StuffedCrustPizza, not a Pizza!

Because margherita uses cls(...) rather than Pizza(...), calling it on a subclass constructs the subclass. This is the main reason to prefer @classmethod factories over hardcoding the class name.

When to choose which

Instance methods operate on self. Classmethods operate on cls and are the standard pattern for alternative constructors that respect subclassing. Staticmethods are plain functions namespaced under a class with no implicit self/cls access at all.