When you see someting, you notice it using your eyes. If you watch someone or something, you look at them, ususally for a period of time, and pay attention to what is happening. To see means to perceive anything in general.
I saw him last night.
I saw an item at an auction site.
They spent a great deal of a time watching TV.
If you notice someone or something, you become aware of them. If you observe a person or thing, you watch them carefully, especially in order to learn something about them
She noticed a bird sitting on the roof.
Public begins to notice climate change.
How to get a rich man to notice you.
NASA invites reporters to observe robotics test in Arizona desert.
She studies and observes the behavior of babies.