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Sponsor - a sponsor justifies and enables the project to become established while overseeing and maintaining co-corporate accountability. The sponsor appoints and finds appropriate support of suitably qualified and empowered project manager and team.
Project Manager - Ensures that everyone in the team understands and execute their role. A project manager is responsible for the success or failure of the project.
A project manager's role is more critical to the success of the project. A sponsor appoints the manager and relies on their skills to bring success to the project. A sponsor will mainly look for ways to fund the project but this does not bring about success. The manager ensures that the project is moving in the right direction and thus responsible for its success of failure.
Please let me know if you need any clarification. I'm always happy to answer your questions.