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Often there's no difference- I took it out of/from my pocket. However, collocation determines that only one can be used in many cases- he comes from Italy.
I think there is some fifference between them when we say: He took his book out of his bag. Here "out of" means "from inside".
Another example with "from".
He took his book from his friend.
out of...from... 
... and the collocations don't follow fixed rules. You can't say "if place-name, then use from" (although that is the more common choice).
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