Free software: Software that comes with permission for anyone to use, copy, and/or distribute, either verbatim or with modifications, meaning the source code must be available. If a program is free, than it can potentially be included in a free operating system such as GNU. Free software is a matter freedom , not price. Proprietary software companies typically use the term “free software” to refer to price. As in the cost of the software included in the price of the machine, or comes with a brand of machines, yet that has nothing to do with the GNU project definition of free software. The term can be tricky so always check to see how the definition “free software” is being used. Is it only a bundle that comes with the computer you have purchased, or is it true free software? True open source free software? Open Source software: nearly all free software is open source, and nearly all open source software is free.
Public domain software: software that is not copyrighted . In special cases the source code is in the public domain, that is a special case of noncopylefted free software, which means that some copies or modified versions may not be free. Sometimes people use the term “public domain” in a loose fashion to mean free or “available gratis.” However, “public domain” is a legal term and means, precisely, “not copyrighted”. its recommended to use the term “public domain” for that meaning only.
The GNU operating system is a complete free software system, upward-compatible with Unix. GNU stands for “GNU’s Not Unix”.
The name “GNU” was chosen because it met a few requirements; first, it was a recursive acronym for “GNU’s Not Unix”, second, because it was a real word, and third, it was fun to say. The project to develop the GNU system is called the “GNU Project”. The GNU Project was conceived in 1983 as a way of bringing back the cooperative spirit that prevailed in the computing community in earlier days—to make cooperation possible once again by removing the obstacles to cooperation imposed by the owners of proprietary software. Every computer user needs an operating system; if there is no free operating system, then you can’t even get started using a computer without resorting to proprietary software. So the first item on the free software agenda obviously had to be a free operating system.