Single-developer license (available only for chosen products) must be purchased for every developer that uses the product in development process. Eg. you have 5 developers, working on the client-server project. Three of them use the product. There is also a person that does Quality Assurance (testing the application). You need a license for 3 developers. Each developer who installs the product and uses this installation in his work, even if this developer doesn't use the product directly, needs a license. NOTE: single-developer licenses are fine for companies and organizations (the name "single-developer" refers to the number of developers and not to the fact, that the developer doesn't have a company)
Company license is a license that allows all developers of the company/organization, who are located in one country, to use the product. In the example above, if three developers work in the same building or campus, you can buy one company license. If one of three developers works in other country, his use of the product is not covered by the company license and you must purchase a single-developer license for him.
Note, that the Company license (except Ultimate license) does not cover the use of the product by your contractors if you outsource part of the project: if the contractor is a separate company/organization, it must purchase its own license. Alternatively you can purchase Ultimate license for the product: this type of license covers subcontractors.
Private business license (available for Callback File System, Callback Filter, CallbackDisk, SolFS and RawDisk) is a special kind of license which is offered to small privately owned companies and startups (usually under 10 people). This license allows use of our software product by one or two programmers for development, testing and deployment (according to the chosen license type). Private Business License is offered at a discounted price.