시계 in Korean can mean any watch or clock. So, it can be a wrist watch, a wall clock, and even a desk watch. If you want to specify that it's a wrist watch, you can add a wrist (손목) in front of 시계. The same goes for other watches/clocks. i.e. wrist watch: 손목시계 wall clock: 벽시계 desk watch: 탁상시계 (this literally means, above the desk watch).