I am a bit confused. There seem to be two different kind of Python packages, source distributions (setup.py sdist) and egg distributions (setup.py bdist_egg).
Both seem to be just archives with the same data, the python source files. One difference is that pip, the most recommended package manager, is not able to install eggs.
What is the difference between the two and what is 'the' way to do distribute my packages?
(Note, I am not wanting to distribute my packages through PyPI, but I want to use a package manager that fetches my dependencies from PyPI)
setup.py sdist creates a source distribution: it contains setup.py, the source files of your module/script (.py files or .c/.cpp for binary modules), your data files, etc. The result is an archive that can then be used to recompile everything on any platform.
setup.py bdist (and bdist_*) creates a built distribution: it includes .pyc files, .so/.dll/.dylib for binary modules, .exe if using py2exe on Windows, your data files... but no setup.py. The result is an archive that is specific to a platform (for example linux-x86_64) and to a version of Python, and that can be installed simply by extracting it into the root of your filesystem (executables are in /usr/bin (or equivalent), data files in /usr/share, modules in /usr/lib/pythonX.X/site-packages/...). You can even build rpm archives that can be directly installed using your package manager.
There are many more than two different kind of Python (distribution) packages. This command lists many subcommands:
$ python setup.py --help-commands
Notice the various different bdist types.
An egg was a new package type, introduced by setuptools but later adopted by the standard library. It is meant to be installed monolithic onto sys.path. This differs from an sdist package which is meant to have setup.py install run, copying each file into place and perhaps taking other actions as well (building extension modules, running additional arbitrary Python code included in the package).
eggs are largely obsolete at this point in time. The favored packaging format now is the "wheel" format.
Whether you create an sdist or an egg (or wheel) is independent of whether you'll be able to declare what dependencies the package has (to be downloaded automatically at installation time by PyPI). All that's necessary for this dependency feature to work is for you to declare the dependencies using the extra APIs provided by distribute (the successor of setuptools) or distutils2 (the successor of distutils - otherwise known as packaging in the current development version of Python 3.x).
https://packaging.python.org/ is a good resource for further information about packaging. It covers some of the specifics of declaring dependencies (eg install_requires but not extras_require afaict).
