What kind of states does Niccolo Machiavelli describe in "The Prince"?

He opens The Prince by declaring that
"all the states, all the dominions under whose authority men have lived in the past and
live now have been and are either republics or principalities." Basically, republics are
governed by a body of elected leaders and are founded on the principle of "a perfect
equality," as he says in his Discourses on Government, and a
population animated by civic virtue. Principalities, on the other hand, are usually
governed by single leaders who rule through the combination of force, compromise,
negotiation, and back-stabbing that he describes in The Prince,
which is only about principalities. It should be noted that in The
Prince, he discusses several different types of principality, which may be
more relevant to the question. They are hereditary principalities, new principalities
(ie those taken by conquest or treaty), constitutional principalities, and
ecclesiastical principalities.