Chiefdoms are how some archaeologists like to classify different polities but this term is so loaded that it cannot properly describe everything that is called a "chiefdom". Traditionally, a chiefdom has a complex society with a centralized power or religion over a people that has surpluses of materials and thus a large power over the area. There is a large problem with this terminology. Some many different social structures can fall under this category, so it makes every place seem the same when they are indeed not. This did not come to light until the study of Cahokia in the past several years. It is considered a chiefdom, but so are many other places that are very different from this epicenter of trade and power. The terminology is very loaded and misleading so the real problem is how do archaeologists come up with ways of comparing societies without having these terms? So far, there's no real solution.
In my opinion, as an undergraduate that is still learning, I think that simply noting the common areas and comparing them is enough. There really is no need to have these different terms like chiefdom, state, tribe, (MEGA-STATE as a graduate student joked this evening). These labels only generalize societies which can make distinctions less obvious to the general public or even archaeologists.
This rant is brought to you by my professor asking me to come to her house for a talk by her husband for her graduate class. I highly suggest his book Chiefdoms and Other Archaeological Delusions.
Side note: I'm dating the other teaching assistant in one of my classes. It's an archaeology romance. <3