What are the forms of government in Animal Farm?
Animal Farm is a satire on the rise and inevitable fall of Communism. When the animals revolt, they draw up new rules on the basis of one Golden Rule: "All animals are equal." However, since the pigs are smarter, they become de facto leaders, and create exceptions for themselves in the workload. Some animals produce more but get the same rations as everyone else; it is discovered that the pigs are taking all the cow milk and drinking it themselves, without sharing it.
"It is for YOUR sake that we drink that milk and eat those apples. Do you know what would happen if we pigs failed in our duty? Jones would come back!"
(Orwell, Animal Farm, george-orwell.org)
This is a classic example of how the leadership in Communist societies rationalizes a higher standard of living for its leaders, even though they preach equality for all. By the end of the book, when Napoleon has lifted himself to the status of honorary human, the farm becomes a totalitarian dictatorship; the fundamental rule is changed to read: "All animals are equal, but some animals are more equal than others." In this manner, the farm has gone back to its original roots, when a human was the dictator over all the animals; the only difference is that an animal has replaced the human.
In a nutshell...
Animal Farm is the story of an imperfect communist revolution. Immediately after the revolution, the animals create a purely communist government but this government is quickly hijacked by Napolean and gradually he changes the rules and the power structure until Animal Farm becomes a totalitarian dictatorship.
1984 is the portrait of a completely dominant, extreme totalitarian dictatorship.
In both books, Orwell was trying to draw attention to the brutality of Joseph Stalin (Big Brother / Napolean) and his abuse of the communist system of government created in Russia and The Soviet Union. The problem with a pure communist regime is that it is a single party state and if that party becomes the enemy of the people, there are no checks and balances to restrict its power.
You list many names for types of Government, there is another one... Stalinism.
And there is an adjective you can use to describe the horrors of Stalinism... Orwellian.