There are tool watches. Worn while doing work which might damage a watch.
There are dress watches. Worn formally or in offices.
Are there any other kinds?
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I would say there's the catch-all category of "everyday watches". This is basically everything else. Not fancy enough to be considered a dress piece, but not for a clearly defined purpose. Like the Omega Aquatera, Tissot PRX, or most watches really.
Pocket watches?