There are many others, but for most
Westerners going to
China, four classes of
visas are of interest:
L -- Tourist
F -- Business
X -- Student
Z -- Work
The L is normally valid for 30 days, but subtypes are valid for 90 and 180 days. 30 and 90 permit 1 entry; 180 permits 2 entries.
The F is normally valid for 180 days, and permits multiple entries, so you can enter on it, then leave China, and enter again within the time of validity, on the same visa.
The X is normally valid for 1 year, and carries with it the right to enroll at an official university. There is no re-entry.
The Z is normally valid for 1 year, and carries with it the right to obtain a work permit. There is no re-entry.
Both X and Z visas require a medical exam as well as a sponsoring organization. They also carry with them the right to obtain a residency permit, but this last item is much less necessary these days -- you can, with only an L visa, legally rent an apartment in most areas of most cities.
You may be interested in Getting a tourist visa for China.