Reflecting umbrellas produce a diffused and soft light due to the larger size of the reflecting surface. They are mounted in such a way that the strobe light is actually facing away from the subject or model. Light flies from the strobe head hitting the inside of the umbrella and then bounces back towards the subject.
There are silver-lined, white, and gold tinted umbrellas. Silver-lined umbrellas are the most efficient and can focus light more narrowly than the other types. White umbrellas offer a wider spread of reflected light, and gold umbrellas produce a warm tone.
Softboxes on the other hand are usually square or rectangular. They are lightweight boxes that come with a reflective inside and a translucent front. Softboxes come in different shapes and sizes and are attached to the front the strobe over the light source. Light emitted from the strobe head gets reflected inside the walls of the softbox and diffused through the box’s translucent front creating a soft, but more focused light source illuminating the model or scene.
Compact substitutes for a power pack/flash head combinations. Their size limits their power, but they are often desired for their portability.
Honeycomb grids, as the name suggests, are basically honeycomb shaped metallic grids that direct the light for a more focused spread. These come in different degrees. The smaller the grid cells the tighter the holes through which the light travels, and in turn the more focused the light becomes.