So what is enough to find on a product (label or else) that makes it truly organic (regulated by USDA). Is "organic" itself means this and it is restricted to put this word on any product that is not organic?
The USDA does regulate a notion of "organic" in the US. Here's their full page on organic certification. Many of the links there are quite relevant. The best one for you is probably the labeling for consumers page, though many others would be informative for you . The Organic Labeling and Marketing Fact Sheet contains more details about labeling restrictions, and the National Organic Program page contains further links including the actual regulations.
In terms of labeling, as described in the linked page on labeling, yes, the USDA regulates the usage of the USDA organic seal:
Unfortunately many other people do have their own notions of what organic means, and if you see the term used without the seal, then you can't really tell what standards it was held to.