There are generally three main different types of focusing screens:
- Split circle with a prism collar
And umpteen variants of each of these. But the first type was more common in film dSLRs and were to aid manual focus. The "split" in the middle would show you how far out of focus you were, and as you adjusted focus, the two sides of the image would align when when focus was achieved, and the prism collar would be evenly illuminated. These types of screens were mostly dropped when autofocus came into cameras, because mirrors in SLRs were no longer 100% efficient--some of the light had to be diverted to the autofocus sensors, and this was done by making the mirrors partially transparent, so that light could then be diverted to the AF sensors (typically in the "floor" of the camera body. Less light meant that the prism collar would be darker, and, well, you had autofocus now, so did you really need the split circle and collar to help you out?
Matte focus screens then became norm, and are in fact the default focus screens in most dSLRs today. The main differences you may find are "high-precision" matte screens, which simply make things a little darker and easier to judge DoF accurately.
Gridded focus screens are an aid in composition. They simply have a grid pattern on them to help the photographer align or position subjects in the composition by the grid.
Many older mid-range and pro end SLR/dSLR camera bodies have the ability to swap focus screens quickly and easily (e.g., my Canon 50D and 5DMkII do this), but these are mostly going the way of the dodo, because of a newer feature--the viewfinder LCD overlay (e.g., the Canon 5DMkIII, 7D, and 70D all have an LCD overlay and do not allow for interchangeable focus screens). Rather than having a physical focus screen that swaps out to do grid lines, an LCD panel is now in the viewfinder lightpath next to the focus screen, and can be used to turn grid lines and AF point displays on and off. Probably because of the possibility of damaging the wiring required for the LCD, most models of cameras that have an LCD overlay in the viewfinder do NOT offer the capability to interchange focus screens, although it's still physically possible to do so (i.e., the LCD overlay is usually physically separate from the focus screen, not integrated into it).