Ducted vent hoods carry smoke and fumes away from the cooking area through ducting, to the open air outdoors.

Duct-Free vent hoods filter smoke and fumes, usually through a charcoal filter, and then recirculates that air back into your cooking area.

Ducted is the more efficient option, as it carries the smoke and pollutants away from you as you're cooking. However, running ducting is not always an option, in which case a duct-free system will still trap grease and odors before recirculating that air back into your cooking space.