Coarse thread drywall screws = best for most applications involving drywall and wood studs. Wide threads are good at gripping into the wood and pulling the drywall against the studs.

Fine thread drywall screws = best for installing drywall to metal studs.
Coarse threads have a tendency to chew through the metal, never gaining proper traction.
Fine threads work well with metal because they are self-threading.