I am pretty sure they do full installs, 40GB on average is pretty big for caching imo, so it must install the entire game (eventually). I think they went for full installs for multiple reasons, noise and speed/performance being the main ones. The PS4 (at least mine) when initially reading the disc is pretty loud which quietens down once it's done doing what it does, I would defo not like that constantly while playing.
As for performance, reading up on it it seems to run at 6x which is 26MB/s (according to various sites), where the stock HDD is 101MB/s read. The size of the games now need the speed that the blu-ray drive is at max just cannot compete with the HDD, which at full speed is pretty loud and is why I assume they didn't do HDD and blu-ray drive.
When you first put a disc in it begins installing what you need to play first, then carries on installing the rest. It's a pretty noticeable drop in volume when it has finished installing. I think once it's fully installed when you put the disc in, it's just checking against what is on the HDD and if it needs to install anything because it eventually shuts up. That's my understanding of it anyway, as after inserting the disc and it finished checking, I never hear it again during the game.
