What is the difference between a UX Designer and a Product Manager?

The title is pretty self explanatory, but the context is that a new project with a small team will need the work of a product manager and that of a UX professional to get the job done. The company, outside the project, has some product manager skills, but very little UX skills. So deciding between a product manager with UX skills and and a UX designer with product manager skills depends partly on where those lines are usually drawn.