Unlike traditional watches, which measure case size horizontally, Apple is measuring the Apple Watch vertically. The smaller of the two has a height of 38mm (specifically, 38.6mm); the larger, 42mm. When it comes to width, the smaller Apple Watch is 33.3mm wide; the larger, 35.9mm.
The Apple Watch Sport shows sport bands for both cases; the Apple Watch and Apple Watch Edition, however, currently list size-specific bands. 38mm-specific bands: Modern Buckle, Hermès Double Buckle Cuff, Hermés Double Tour. 42mm-specific bands: Leather Loop. Hermès Single Tour Deployment Buckle. Other types of bands are the third party manufactured bands.