On a super-low budget film, everyone wears more than one hat. But when you start working on larger projects, you have treat these departments separately. Here are some basic tips to help you sort them out.
Handles the camera and anything attached to it (tripod, lenses, drives/film/tapes, filters, videotap/monitor), with the exceptions of a dolly or mount/rig (handled by the grips), and the video playback gear. The Director of Photography is in charge but I typically deal with the camera operator or 1st AC. The 1st AC focuses and changes the lenses, filters and supports, the 2nd AC cleans and organizes the gear and helps out the 1st, and the loader downloads the media from the camera. On a union shoot the DP does not typically operate. A Digital Image Technician (DIT) works with the DP to set the look. On RED shoots the DIT often doubles as Loader.
Responsible for lighting the set and handling the electrical needs of the shoot. This includes running generators, setting up breaker box tie-ins, and running cable from the source to the lights, office, trailer(s), holding, video village, and/or department areas. Electricians put up, focus scrim and gel lights and reflectors. The Gaffer is the department head. The Best Boy Electric is the Gaffer's assistant. The Genny Op runs the generator. Subordinates are referred to electrics. The soundstage house electrician runs power to the set construction crew and the department offices. A swing grip/electric works for both departments, depending on the need.
Responsible for set safety; scaffolding construction; dolly, jib or crane operation; and shaping light through flags, nets, silks, or other means. Grips set up car rigs and specialized mounts. An electric sets up a light; a grip puts things in front of it to shape it. The Key Grip heads the department. The assistant is the Best Boy Grip. The Dolly Grip handles the dolly. Subordinates are referred to as grips.
A version of the grip and electric departments, structured the same way. The riggers work ahead of the shoot crew to set up lighting at the next location. De-riggers take down the gear at the last one.
The Bests usually come up with the final equipment lists, and are in charge of the checkout and return. Often you'll rent the grip and electric gear (and dolly) from one vendor or from one of your own crew. On a big enough shoot, each department gets its own truck. On smaller shoots, the departments will share. Keep the camera on a separate truck!
The Bests and 2nd AC are in charge of their departments' paperwork - payroll forms, timesheets, deal memos, equipment orders, etc. The Loader hands in the reports and media. The DIT or DP sometimes hands in color correction notes or scene files.
Usually the crew elects one of the Bests to be the shop steward to represent them on the shoot. The shop steward reviews the deal memo, and comes to the production manager with paycheck discrepancies, meal penalty warnings or other problems.
The DP works out a high-level lighting plan. The Gaffer and Key Grip figure out how to execute it. The Bests work out the manpower and sometimes the gear. The camera operator sets the frame, the 1st AC sets focus marks, and the dolly grip drives.
While this division of labor may seem strange, it makes sense on larger projects. The equipment and skills are very different. The clear delineation between chores make things go more smoothly on set.