Others will answer shortly but it looks to me that the first one is the Easyup hood which, when down, sits folded up on top of the rear body behind the seats. It has the advantage of being able to be put up quickly in case of necessity.
The other hoods that have a lot of press studs at the top of the screen and around the rear of the hood are the "traditional" style hoods. They are much more fiddly to put up but when down the hood and the hood rails can be stowed behind the seats leaving the car with a much cleaner appearance (no folded up hood in sight). In the case of really fine weather it could even be left at home.