Categories in French are already not so well defined, but their translation in English is probably not good.

It may be "sport" instead of "sporter" indeed (it is the case in the French version: "sportive").

"Trail" is a bike which can be used on both road and off-road, I am not sure that the name is the same in English
http://fr.wikipedia.org/wiki/Trail_(sport)
It seems to match the "dual purpose" category then.

I am not even sure if that "All-Terrain Sports" is supposed to be off-road or not... we really need some bike experts to help here