What is the difference between shared hosting and VPS?

It is the same difference as between a dedicated server and usual shared hosting.

With a VPS, you receive all the power of dedicated hosting with the ability to have your own set of services and customizable disk space. With shared hosting, you have limited administrative access and can’t customize software configurations, while with a VPS you can perform any actions from your control panel and don’t need to contact technical support with every single request.