The tar.gz file is a source archive whereas the .whl file is a built
distribution. Newer pip versions preferentially install built
distributions, but will fall back to source archives if needed. You
should always upload a source archive and provide built archives for
the platforms your project is compatible with. In this case, our
example package is compatible with Python on any platform so only one
built distribution is needed.
See: https://packaging.python.org/tutorials/packaging-projects/
You would typically not manually create the source archive and wheel, but use setuptools and wheel to do so for you.
Nowadays, many packages are wheels. While installing these wheels using pip, pip will:
[…] unpack the archive in your current site packages directory and install any console scripts contained in the wheel.
See: https://wheel.readthedocs.io/en/stable/user_guide.html#installing-wheels