Well, it depends on the production, and how the hierarchy is arranged (often defined by the producer).
In very general terms, the Cinematographer is the Camera Operator - the person behind the lens.
The Director of Photography might also be the Camera Operator, but on larger productions, is probably a guy sitting in a chair behind the Camera Operator, seeing the "big picture." The DP, or maybe the Camera Operator will also interface with the Gaffer(s) to set up all lighting to a mechanical level, but with a style (to create a mood), per the DP' idea of what the Director will want.
The Director is often a separate entity, and directs the actors, works with the Camera Operator, or DP, to get everything functioning, as he/she wants.
The term Filmaker can be a catch-all, for the roles of those mentioned above, and will not be an official title for any person on the production crew. That term is often applied to a person, often wearing many hats, or might be applied to any of the roles above.
Remember, those terms are not set in stone, and with a small production, one person might play all roles, and might also be referred to as the Filmmaker.
Good question,
Hunt
