Depending on the task at hand and the tools available, there are different styles of screws to choose from.
First there is the slotted vs. the Phillips head. A slotted screw head is used with a flat-head screwdriver (a.k.a slotted-tipped, straight-tipped, flat-blade, etc.) A slotted screw has one groove going straight across the head for the screwdriver’s tip to fit into. (1)
A Phillips screw head has a plus-sign shaped groove made to fit a Phillips tip screwdriver. The Phillips tip screwdriver is a fairly new screw from the 1930’s designed to prevent over torqueing. It did this by the shape of the grooves which caused the tip of the screwdriver to slip out before too much torque is applied. The screw is also easier to screw in and less force is needed embed the screw. (2)
Besides the two basic grooves, there are many different shapes the screw head can take including flat, round, oval, pan, truss, fillister, and hex. The shape used depends on the project.
1. Builder’s Comprehensive Dictionary (Robert Putnam, Reston Pub. Co., c1984) p.370