Obviously they are synonyms, with very close meanings, but in everyday speech: 1. Look-A general term, "I am looking at the sky" but you don't tell me anything very specific. 2. Watch-"I am watching the sky". I am watching or looking for something specific, I am waiting for the sunset, or to see a meteor, of watching the cloud formations to see them change. 3. See- Another general term. " I see the sky" Mostly this would be used if there is some question about whether you can see something. " Did you see the beautiful sunset last night?" "Yes I looked out my window and I saw it. I watched it for 15 minutes."