PS4 has a much better low power mode, in which it will totally shut down main APU and memory [it will leave them enough power just to not loose data they are holding] and main fan. The entire operation of PS4 then is taken over by secondary lowpowered background chip that is monitoring the internet, wifi, and has access to the HDD. That secondary chip will update your games, download you games [when you buy them via the smartphone/PC browser/Vita], and it will start up PS4 when you request it via Vita Remote Play.
So... Every time when you shutdown PS4 it will emit zero noise [maybe HDD a little when it is its unpacking/installing some package], core OS services remain active, things are happening, waiting for your input. You can only get full shutdown if you pull the power plug from the wall.
Btw, thanks for noticing that this is missing from OP. I will add it in the FAQ.