The names are a bit confusing.
The daisy seed is a development board, like an Arduino or a teensy, but specialised for DSP. It has its own datasheet, different from the patch submodule one you linked.
Daisy Patch is a eurorack module that uses the daisy seed development board as it’s ‘brain’. The module itself adds a bunch of hardware between the knobs and jacks and the daisy pins, so, for example, the 10v P2P eurorack audio signal doesn’t fry the seed with over-voltage.
Daisy patch submodule is also a development board, I believe it uses the same core chips as the seed, but the board adds extra hardware specially designed for interfacing with eurorack. This means it’s powered by eurorack PSU (+12v and -12v) and it’s pins are designed to accept eurorack level audio and cv, voltages that would fry a seed.
The patch init() is a eurorack module that uses the patch submodule as it’s ‘brain’. It doesn’t add any active hardware, it’s simply some knobs and jacks connected directly to the patch submodules pins.