A watchmaker is one who primarily repairs watches, although historically this person also made watches. A contemporary, well-trained watchmaker is more likely to be able to repair a wristwatch or a pocketwatch than to actually build or manufacture a watch from scratch. Watchmakers can typically manufacture many of the parts found in a wristwatch or a pocketwatch.
A watchmaker, as the name infers, works primarily on watches, not clocks. Some watchmakers work on clocks, but the skills and tools needed to work on a watch aren't always applicable when working on a clock.