The difference between "see" and "watch" is that we normally "watch" something that occurs over a period of time, as opposed to "see". We watch athletic events, for example. We watch television. "Watch what happens when I light the fuse".

To see something is to view it, more casual and unintentional. Such as did you see that bird fly by? 'Watch' is done with intent, you are watching that person/ object on purpose. "Such as i watched her while she walked past me" or "I watched the television".

Watch - look forward see - receive visual information