Is there any difference between these two phrases? For example, "Look out for pickpockets" and "Watch out for pickpockets", which is correct?
I think "watch out" is more defensive. "Look out for pickpockets" would mean: "try to spot/identify pickpockets", and "watch out for pickpockets", "be careful, proctect yourself against them". Well, that's how I understand it...
Personally, I use "watch out for" exclusively in that context, i.e., when the idea is to be on guard against someone or something. Many people do substitute "look out for", but I'm not one of them!

I use "look out for" mostly in the context of self-interest: "You've got to look out for your own interest." Here "look out for" means "take care of".

In a slightly different context I use the phrase "be on the lookout for", but then it means "be alert to the possibility that someone or something may appear", not necessarily "be on guard". "As I read my grammar book, I was on the lookout for unusual constructions with adverbs."

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Look out can be good or bad (look out for your family)
You means that these two sentences are all correct, do you?
I think they are the same which means " be alert or watchful in order to see or find something or person. " for example, will you go to the club and look out for John ? The cops were asked to watch out for suspicious bags on subway.
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