Aristotle distinguished six kinds of social structure in three pairs:
A state with only one ruler is either a monarchy or a tyrrany;
A state with several rulers is either an aristocracy or an oligarchy; and
A state in which all rule is either a polity or a democracy.

In each pair, the first sort of state is one in which the rulers are concerned with the good of the state, while those of the second sort are those in which the rulers serve their own private interests. (Politics III 7) ***

Is "the good of the state" assumed to be "the common good"?

Of course. And the common good must include the able, the healthy, the disabled, the sick and suffering. The selfish and greedy must be left to their own doing as long as they do not infringe on the common good. Are the sick and suffering, the selfish and greedy?