The first difference is that look is usually followed by the preposition at. Also, there is a difference in the amount of time. When you look at something, it is often quick. Sometimes we can look at something for a longer period of time, but that leads to the final difference: we often look at something that isn’t moving or static.
Look at this cool website!
I went to the museum to look at the beautiful paintings.
Look at that guy over there! He is doing a head stand!
Watch is not followed by a preposition; you have the object of your attention after the verb. Watch is often for a longer period of time than look at because we watch moving or changing things.
I watch TV too much!
You have to watch those dancers over there in the park. They are really good!
Watch where you walk please! You almost ran into that garbage can!
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