Proprietary software, as defined by the Free Software Foundation, means any software that is not free software or is only partially free. The modification, use and redistribution is prohibited, or requires express permission the originator. Non-free is a customary designation for software that fails the Debian Free Software Guidelines, which follow the same basic idea of software freedom and on which the Open Source Initiative definition of open source is based. Proprietary means that some individual or company holds the exclusive copyrights on a piece of software, at the same time denying other people the access to the software's source code and the right to copy, modify and study the software.
The term proprietary means "privately owned and controlled". Hence software can remain proprietary even when source code is made publicly available, if control over use, distribution, or modification is retained (e.g., the commercial version of SSH and the Microsoft Shared source licence programme.) On the other hand, software is considered non-proprietary once it is released with a license that would permit others to "fork" the software and release their own modified versions without onerous restrictions, even though the copyright may remain in the hands of a single individual. At least in theory, control has been conceded.
It is important to emphasise that many types of software that are offered for free are proprietary, such as freeware, shareware and abandonware. This is because the source code in those distribution schemes is closed, or modification is prohibited, or redistribution requires express permission of an individual, organisation or company.