* one that puts emphasis on democracy,
* another that puts emphasis on liberalism.
I forgot the exact terms for them, especially the second one. The basic difference is that the first one says any action is valid as long as it was democratically chosen. The second says freedom of one person ends where freedom of the next person starts. Otherwise, anything goes. The second one has high respect for laws, constitution and institutions, in an attempt to assure the system doesn't degenerate. Ancient Athens were an example of the first, Sparta - regarded as the realized utopia by ancient Greeks - example of the latter.
It is perhaps little known that USA's Founding Fathers had more faith in Sparta's system than the Athenian one. Things we (the western civilization, broadly speaking) owe to Sparta are: strong costitution, president (2 kings in Sparta), ministers (ephors), senate (Gerusia; council of elders had the strongest power in Sparta), the lower house ouf the parliament (Apella, gathering of all citizens above the age of 30), although you might argue Apella was closer to common voting.
There's a morbidly fascinating series about Spartans by the History channel. I highly recommend it. They had a really unique political system, resembling BOTH fascism and communism.
But I digress. Democracy, without laws and institutions acting as safeguards, is a cruel system. I remember there were only a couple of years Athenians DIDN'T vote to open a year by starting a war. Without safeguards, if someone is disliked enough, he can be sentenced to death and you don't need a proof. Athenians did that to Socrates, because he was unpleasant to be around due to his biting critique. Athenians also had a system where officials and judges were assigned to their posts literally at random, using a lottery machine with marbles. The same person could be charged in a court and some time later assigned as a judge in his own case. Talk about conflict of interest.