What is the difference between len() and sys.getsizeof() methods in python?

They are not the same thing at all.

len() queries for the number of items contained in a container. For a string that’s the number of characters:

Return the length (the number of items) of an object. The argument may be a sequence (string, tuple or list) or a mapping (dictionary).

sys.getsizeof() on the other hand returns the memory size of the object:

Return the size of an object in bytes. The object can be any type of object. All built-in objects will return correct results, but this does not have to hold true for third-party extensions as it is implementation specific.

Python string objects are not simple sequences of characters, 1 byte per character.

Specifically, the sys.getsizeof() function includes the garbage collector overhead if any:

getsizeof() calls the object’s __sizeof__ method and adds an additional garbage collector overhead if the object is managed by the garbage collector.

String objects do not need to be tracked (they cannot create circular references), but string objects do need more memory than just the bytes per character. In Python 2, __sizeof__ method returns (in C code):

Py_ssize_t res;
res = PyStringObject_SIZE + PyString_GET_SIZE(v) * Py_TYPE(v)->tp_itemsize;
return PyInt_FromSsize_t(res);

where PyStringObject_SIZE is the C struct header size for the type, PyString_GET_SIZE basically is the same as len() and Py_TYPE(v)->tp_itemsize is the per-character size. In Python 2.7, for byte strings, the size per character is 1, but it’s PyStringObject_SIZE that is confusing you; on my Mac that size is 37 bytes:

>>> sys.getsizeof('')
37

For unicode strings the per-character size goes up to 2 or 4 (depending on compilation options). On Python 3.3 and newer, Unicode strings take up between 1 and 4 bytes per character, depending on the contents of the string.

For containers such as dictionaries or lists that reference other objects, the memory size given covers only the memory used by the container and the pointer values used to reference those other objects. There is no straightforward method of including the memory size of the ‘contained’ objects because those same objects could have many more references elsewhere and are not necessarily owned by a single container.

The documentation states it like this:

Only the memory consumption directly attributed to the object is accounted for, not the memory consumption of objects it refers to.

If you need to calculate the memory footprint of a container and anything referenced by that container you’ll have to use some method of traversing to those contained objects and get their size; the documentation points to a recursive recipe.