Traps are sized and sets built for each specific species being trapped. You are refering to steel jaw traps. Yes, trappers still use them. Personally, I prefer the conibear traps. For all things trapping related, see
Buckshots Camp. Buckshot Hemmings has been trapping his whole life (I think). He is so good that he could probably trap his own shadow. His instructional DVDs will teach you everything you need to know. He also sells kits designed specifically to produce food.