...I'm wondering what is the difference? Are the drywall screws made of a more brittle metal? Are the wood screws tapered?
Yes to both. In addition:
1)Drywall screws have a "bugle head", and not a flat head. The bugle head doesn't fit as well in a properly countersunk hole in wood (it is designed to self countersink in sheetrock without tearing the paper).
2)Drywall screws have a tip meant to pierce the paper in drywall (and drill and tap into a metal stud). Wood screws have a gimlet tip meant to grab wood and self feed.
3)Wood screws often have a non-threaded section near the head. This not only helps with shear strength once assembled, but also prevents the head from twisting off, and lessens separation of parts being screwed together (though that last bit is not necessarily a big problem in parts properly fixtured).
In projects "where it counts", I use "cabinet screws" and not drywall screws in wood. Drywall screws are for drywall.