An agency is a business which provides a service on behalf of another business. For example, the agency recruits other companies to provide a service for their client company.
A contractor is a business which provides a service to the agency’s client for a set period or for the duration of a project. The business paying the contractor has the right to control or direct only the result of the work and not what will be done and how it will be done. An independent contractor is self-employed.
Finally, the subcontractor is a single person, a team or a business which could possibly have a field of expertise or experience for a particular field that they are hired for within the contract.
For example, an agency may be asked to find a business which can extend their client’s offices. The recruitment company (agency) would find a few companies that could potentially do that for them. Once the agency’s client has chosen the construction company (the contractor), if the construction company is unable to fulfil the whole job using their employees, then they may look to find someone (a subcontractor) to help them out for this one project.