Wood screws are better than drywall screws for woodworking projects. Drywall screws are made of hardened, brittle steel, and the shaft will often snap during installation, especially if they're screwed into hardwoods. That can be a disaster when you're working with finished material and you want to remove the screw to reposition something—it's nearly impossible to get the broken-off shank out of the wood without damaging the surface. Drywall screws are hardened so that the Phillips slots won't strip out under the stress from high-speed screw guns. Wood screws are thicker and made of softer metal, making them more snap-resistant.
Different thread patterns make the screws work slightly differently too. Wood screws are smooth rather than threaded just below the screwhead. The smooth section of the shank slides by the top half of the wood so the head of the screw and the threads can more or less clamp both pieces of wood together.
Drywall screws are threaded nearly all the way to the head. When you use a drywall screw to fasten two boards, the top threads will anchor in the top board and sometimes actually keep the two boards apart unless the two pieces are tightly clamped to begin with.
The bad news is that using wood screws requires a little more prep work. You not only need to drill a pilot hole for the threads but also a wider counterbore hole the length of the unthreaded shaft and then a countersink hole for setting the head. Sound like a lot of work? Just buy a set of three countersinking bits and they'll handle all three drilling chores at once for most common screw sizes. No more excuses for using the wrong screw.