Definitions from Webopedia
Interoperability: The ability of software and hardware on different machines from different vendors to share data.
Proprietary: Privately owned and controlled. A proprietary design or technique is one that is owned by a company. It also implies that the company has not divulged specifications that would allow other companies to duplicate the product.
You can see a real world example of interoperability with consumer electronics. A user can buy a Phillips TV, plug it into a Toshiba DVD, add speakers from Bose and play a Sony DVD from Japan to watch a movie made in Hollywood and it all works together.
For an example of a typical proprietary system, consider the imaginary digital radiography system, ProprioRay. It will only work with the ProprioRay sensor plugged into a ProprioRay connector. The image can only be captured and displayed using ProprioRay software and images are stored in a proprietary ProprioRay format.
More recently we have been introduced to the imaginary CAD CAM system Ceroscan. You can only use a Ceroscan camera plugged into a Ceroscan computer running Ceroscan software. You can not transfer the digital impression to another software or to a mill or lab of your choice you must use a Ceroscan mill and Ceroscan approved labs. Ceroscan even has a restricted version of the Internet you must use with their products.
Manufacturers like proprietary systems. Consumers prefer interoperability. Experience has shown that vendors will attempt to maintain control unless consumers demand interoperability. When you do they will try and tell you why it is actually to your benefit that they keep you hostage in their private garden.