Software is either free of charge, or it isn't. The difference is mainly an idealistic one. Non-free software is sold (or distributed in the hope that a payment will be made) by a person or company who is trying to make a profit. (Or save up enough to eat, in the case of full-time shareware authors.)
Free software is either obligation free (e.g. public domain) or just freely redistributable. The latter category is arguable the best, because it protects the the rights of author(s) and encourages respect for the work that has been put into the development of the software. (Hopefully the author(s) distributed the software under a licence that suited their needs without unduly restricting its use.)
Open Source software is a special category of Freely Redistributable Software for which the source code is available. Some licences allow the source to be modified and/or redistributed.
F/OSS is an umbrella term used describe not just software that is free and/or open, but the dual phenomena of its production and use.