Originally drywall screws were fine threaded and intended for commercial construction. Home construction used nails to tack drywall to boards. The use of drywall screws in home construction quickly became popular because the screws have better traction and go into studs faster.
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Fine thread screws are intended for use in commercial construction or in a structure with metal beams. Coarse thread drywall screws are intended for residential construction or in a structure with a wooden frame.
The tip on a fine thread drywall screw is sharper than the tip on a coarse thread screw. This is so that is will more easily pierce metal. As a result it takes less physical pressure to start a fine thread screw.
A coarse thread drywall screw has fewer threads, or more space between threads, than a fine thread screw. As a result they have a slightly higher pull-out resistance than fine thread drywall screws. Coarse thread screws, as a result of their lower thread count, also screw in faster.