I'd like to know the different meanings of see and watch and the typical uses of these two verbs.
See / Watch
Seeing is noticing something or somebody with your eyes, usually with no explicit intention or purpose behind the action. If you watch something or someone, you look at them deliberately, usually for a longer period.
Watch is often used with progressive tense forms. See is not used with progressive forms, but may be used with can to suggest something in progress. Compare the following:
Can you hear me at the back? Am I speaking loudly enough?
I could hear a dog barking but apart from that there was no sound.
I'm surprised to hear you say such awful things about her. I thought you liked her.
I could hear them talking in the next room, but I tried not to listen to what they were saying.
You need to listen to the tape very carefully if you want to understand what she is saying.
I didn't hear the phone ringing because I was listening to a Mahler symphony on the radio.
See / Hear + that-clause
We often use I hear and I see with a that-clause to indicate that we have noted something or that we understand or gather that something has happened or will happen.
I hear / understand / gather that you're planning to quit your job with IBM and go freelance.
Have you heard that Jenny's gone freelance? ~ No, I've heard nothing about that.
I see / understand / gather that the postal workers are threatening another one-day strike in October.
I can't see / understand what all the fuss is about. It's only a one-day strike.
Note these further, more specific uses of see and watch:
see = meet (note that in this meaning progressive forms are often possible)
I'll see you outside the hospital at eleven o' clock.
He's seeing the doctor about his bronchitis tomorrow.
I'm sorry, but he's not well enough to see you now.
She must really stop seeing him. He has a bad influence on her.
see = find out (note progressive forms never possible)
I'll go and see if I can help them.
He went back to see if they needed any help.
As we saw when he went back to help them, these guys are totally independent.
see = accompany
You may not be able to find your way out. I'll just see you to the door.
He's old enough to come home by himself, but can you just see him across the busy road?
watch = be careful about ...
We must watch the time or we shall be late.
Watch that you don't spend too much money in Oxford Street. Watch your purse too. Watch out for pickpockets.
watch = look after
Can you just watch my bags while I go to the loo?
You may also watch your weight if you decide to be careful about the things you eat or watch the world go by, if you stand or sit somewhere and watch people as they pass by.