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.
"The first three words of the Constitution, "We the people," express the principle of popular sovereignty. According to this principle, the people rule. They hold the final authority, or ruling power, in government."
The powers of the ruling class in a government called an oligarchy, allow the rulers to basically rule as they see fit. Members of this ruling class have one main important responsibility, which is to remain in power and prevent any revolutions to destroy the oligarchy.