Isn't range hood with filter top fan better?
The slats are louvers which cover the entrance to the housing and prevent the blower from accidently ingesting things like paper towels or hands stuck up there. The small knobs on them are spring loaded levers which allow for removing the three panels for washing. Filters, in the sense of actually cleaning the air are uncommon because you wouldn't want a flammable substance like foam or paper catching grease. Instead there's usually some metal mesh or trap to catch grease which periodically needs cleaning. 

In your particular case, the second model is superior. Grease is going to be mainly confined to the louvered panels which can be removed and chucked in the sink. (Possibly dishwasher if you're adventurous.) It probably also uses a blower rather than radial fan for higher airflow. I imagine the first is cheaper.

To answer your final question the fan is above the panels, but it's probably inside a large plastic baffle which reduces the rectangular opening down to a smaller round hole. It's along the same lines as a vacuum cleaner, which has a large square opening to clean with and a smaller round exhaust at the bag, with a fan in the middle. The difference being that the fan and exit in this case are still several inches in diameter. (The "fan" may be a centripetal blower too, to provide better airflow. Think leaf blower rather than desk fan.)

Incidentally, your existing fan also requires internal ducting because it can be installed with either top or back exhaust. The difference is that the fans are in the front of the ductwork.