• Any Python file is a module, its name being the file's base name without the .py extension.
• A package is a collection of Python modules: while a module is a single Python file, a package is a directory of Python modules containing an additional __init__.py file, to distinguish a package from a directory that just happens to contain a bunch of Python scripts. Packages can be nested to any depth, provided that the corresponding directories contain their own __init__.py file.

The distinction between module and package seems to hold just at the file system level. When you import a module or a package, the corresponding object created by Python is always of type module. Note, however, when you import a package, only variables/functions/classes in the __init__.py file of that package are directly visible, not sub-packages or modules.

Example

As an example, consider the xml package in the Python standard library: its xml directory contains an __init__.py file and four sub-directories; the sub-directory etree contains an __init__.py file and, among others, an ElementTree.py file.

See what happens when you try to interactively import package/modules:

>>> import xml
>>> type(xml)
<type 'module'>
>>> xml.etree.ElementTree
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'module' object has no attribute 'etree'
>>>
>>>
>>> import xml.etree
>>> type(xml.etree)
<type 'module'>
>>> xml.etree.ElementTree
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'module' object has no attribute 'ElementTree'
>>>
>>>
>>> import xml.etree.ElementTree
>>> type(xml.etree.ElementTree)
<type 'module'>
>>> xml.etree.ElementTree.parse
<function parse at 0x00B135B0>

NOTE

In Python there also are built-in modules, such as sys, that are written in C, but I don't think you meant to consider those in your question.