That's correct! Public Interest Registry is the in-charge of .ORG domains. '.ORG' domain must be submitted to it for verification. Web registrar will send it automatically after your register the .ORG domains. These domains are for non profitable organization, educational firms etc.
The domain .org is just a website for non-profit organization so it means you cannot use it with your business or else your site will be terminated. As far as i know no one have ever used .org extension for online money earning purposes.
The top level domain .org is traditionally been registered by not-for-profit organizations like charities and industry groups. However, anyone may register a .org domain for any purpose these days, at least from what I learned. There are no restrictions on ownership for .org domains. Many for-profit companies use .org domains to contain philanthropic or other social ventures.