The difference between these verbs is very clear.
'See' - is a sense. Hearing is another sense. The five senses are sight, touch, smell, taste and hearing. Seeing is involuntary. If you are not blind, and you have your eyes open, you can see.
'Watch' and 'look' are actions, in the same way that 'listen' is an action. They are voluntary. You choose to watch or to look at something. If you watch something you are paying close attention to it. You watch things which are moving or likely to move.