cinematography is the art and also the technology of photography for film, involving things such as composition, as well as lighting, location, etc.

cinematographer is the person who presides over the camera and light crews in a film, and are responsible for the filming of the scene

the difference between a director and cinematographer is that a director oversees and gets the final approval, the director overviews the overall composition and how it fits into the final film, as well as overviews the whole production whereas the cinematographer mainly takes care of the technical side and the camera