Bakster
Also, you mentioned the net is drug along the bottom. Is that literally pulled along the seafloor? You'd think it'd snag on something.
Largely, you frag for bivalves--oysters, scallops, and the like.
The net has a toothed frame designed to "chatter" on the bottom. And, it's a small affair, perhaps a meter wide.
The draggers also "know their bottom," they don't drag where they get snags or the like. (This is also a benefit of being under sail--no ripping the winches out or the like.)
Shrimp trawlers have their nets just above the bottom. In days of old, there was a "necklace" with dangling chains ahead o the net, to "spook" the shrimp up off the bottom. This is not allowed in modern fisheries.
The skipjacks Bill notes use a pushboat to get to the fishing ground, but are olny allowed to "dredge" under sail-this is to protect the oyster beds. The pushboats don't have rudders, as they are lashed to the sides/sterns o the skipjacks.
A limited number of powerboats are allowed out on the oysterbeds, but, they are restricted to "tong-ing" for their catch. The tongs are set up like a pair of 1m wide rakes with 3m hafts, pivoted like scissors. You want to be a stout fellow to work the tongs and raise enough fresh oysters to make a living of it.
The North Sea trawlers, like the Tigers, made their living in the mid-depths, going after specific speies of fish--like herring or hake or the like.