Impur, Yes they are similar in some ways. They do use air as the means to run the filtration. The sponge filter is just that a filter that is made of a sponge, while a box filter is a container type filter where you put gravel and filter floss in and hook the air line up to. I use each in my 29 gal tanks and I can tell no real difference between the sponge and the box. Both keep my water very clean and both are easy to maintain.
Sponge filters will run a bit more, maybe 3 or 4 dollars but thats not real bad
HTH
Les