some dict's special methods

[buran]

does it means that behind every dict's built-in method stay one dict's special method?

No, I don't know how you come to that conclusion. As it state in the docs

A class can implement certain operations that are invoked by special syntax (such as arithmetic operations or subscripting and slicing) by defining methods with special names. This is Python’s approach to operator overloading, allowing classes to define their own behavior with respect to language operators.

That's true for every class, builtin or custom.

>>> dir(dict)
['__class__', '__contains__', '__delattr__', '__delitem__', '__dir__', '__doc__', '__eq__', '__format__', '__ge__', '__getattribute__', '__getitem__', '__gt__', '__hash__', '__init__', '__iter__', '__le__', '__len__', '__lt__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__setitem__', '__sizeof__', '__str__', '__subclasshook__', 'clear', 'copy', 'fromkeys', 'get', 'items', 'keys', 'pop', 'popitem', 'setdefault', 'update', 'values']

e.g. __str__ is called when you do str(some_dict)
special methods are methods/attributes, there is no other front-line methods/attribute