Plutocracy is the "rule of money": rich people dominate society and politics.
Oligarchy is when a few people share political power, at the expense of everyone else.
Aristocracy, although it can be an oligarchy, is the rule of the elite, under a social class system. Most often it is used to refer to the rule of royalty or nobility, although some say money is forming a new aristocracy.
A bureaucracy is a form of government in which the large number of small officials (who work their way to becoming useful officials through tests) work under higher officials to provide efficient ruling of a large area. This was mostly used in pre-20th century China.
They are all different types of government
An oligarchy
Oligarchy is government by the few. Plutocracy is government by the wealthy few.
The wealthy rules
Some names for the form of government ruled by the rich or powerful might include, a plutocracy (rule by the wealthy), an oligarchy (rule by the wealthy, connected, educated, royalty), or maybe an aristocracy (rule by a small class of privileged).
Government by the few is an oligarchy, by a single powerful ruler an autocracy, and by the landed gentry an aristocracy.
Yes. The idea behind a Republic is that all matters of state are considered a public matter, and those voted into office are done so by election. An oligarchy isn't a "proper" form of government - it simply states that power rests in the hands of a small, select group. This could be a monarchy, hierarchy, aristocracy, plutocracy, etc. Even a Republic can be a de factooligarchy.
An aristocracy government was ruled by one King/Queen, an oligarchy government was ruled by the few.
An oligarchy is a government controlled by a small group of wealthy landowners and corporate leaders.
Oligarchy
Democracy is (theoretically) governed by all of the people. An oligarchy is ruled by a small group of people... as "oli-" means "few." Some might argue that the broken democratic system of the US is creating a specific type of oligarchy called a plutocracy, which is when the wealthy rule.
An oligarchy is when the power is in the hands of a few people. An aristocracy is a very powerful group. Usually the ruling power is in the hands of a few people, specifically rich people. They are alike because the ruling power is divided into a few people.