From my experience, you will find mostly a matrix structure in larger organizations. All the large organizations I have worked with have followed this model. This may be in part because I have worked in companies involved in multiple projects.
Small organizations are often able to use only a functional model. This may be looser than you find in a larger organization as some people may work in multiple functional roles. Their projects tend to be small enough that they don't require a project organizational structure. If they do have a large project, it tends to involve the entire company, so that it can be run without a separate organization structure.
As I noted in my previous response, career development is usually managed using a functional organizational structure. Some people in the organization will move from one functional role to another. The organization may encourage this in people they are grooming for management. In other cases, people may decide that they would prefer a different role, either temporarily or permanently. Some functional roles like project management may not have entry level positions, so people need to start in a different functional role initially.
Projects requiring a team usually have their own organizational structure. Many projects require resources from various functional streams, so that they are difficult to manage within the existing functional organization structure. Large projects can run for several years, and develop their own organizational structure. However, by their very nature projects end, so this is not a good organization structure for a company.
Well managed organizations use their functional organization structure to share information and skills across projects. Other start each project as if they had never done a project before.