All PS4 and Xbox One installs are the entire game on the HDD.
That's what I thought too, but when I popped Puyo Puyo Tetris in my PS4 for the first time a few days ago, it was done "installing" within about 10 seconds. I know the game is not *that* small. Maybe it's possible that some PS4 games can run off the disc? Or did it just complete the install silently after the progress bar filled and disappeared?