'See' is a sense. We have five senses - see, hear, touch, smell and taste. We often do these things involuntarily. If your eyes are open you can see. If it isn't dark, you can see. To see is not an action - it is a sense and an ability.
'Watch' and 'look (at)' are actions. We do them voluntarily. We generally watch something that is moving (or likely to move), and we look at something that is static.