"Professional Staffing" firm is a company, market maker that makes a living from matching the clients' need, in the form of jobs or projects that usually have a predefined time and/or scope, with the necessary human resource such as a highly skilled independent professional who has the appropriate experience, skills and knowledge to execute the task.
The independent professionals are NOT employees of the staffing firm, they are independent, free agent who can work for anyone else. A contractual relationship is formed only when the staffing firm finds a project for the independent professional, i.e. a contract between the staffing firm and the client, a matching contract between the staffing firm and the independent professional on a pre-agreed daily rate called "per diem".
That means, the staffing firm makes a handsome margin of reselling the independent professional's time to the client. Typically 30-50%.
Unless the independent professional is a super-star and in a hot industry that is always sought after by the staffing firm's clients, otherwise, the independent professional should not rely on the staffing firm as its only source of work. The independent professional must be able to develop its own client.
Some staffing firms will pre-qualify the independent professionals by interviewing them or even background check, some don't and will only do so if a potential project materializes.
Some staffing firms take responsible of the quality control of the project and may dedicate its own resource to oversee the project, some don't.