Oligarchy means "the rule of the few" and monarchy means "the rule of the one". In Monarchy, Monarchs were often absolute in their power and were unconstrained by either legal or political limitations. The Magna Carta was demanded from the King by England's landowning aristocracy who wanted definite and permanent legal limitations on royal power. Magna Carta was revised many times (1216, 1217, and 1225), guaranteeing greater rights to greater numbers of people, thus setting the stage for English constitutional monarchy.
Over the centuries, England's monarchical system became gradually transformed to the modern constitutional structure where the monarch possesses only formal legal power that must, by political convention, be exercised only with the advice and agreement of the monarch's ministers.
These ministers are chosen by a Prime Minister who the monarch appoints but who, by political convention must be the party leader whose party commmands majority support, or the most support, in the elected House of Commons.
The convention that the monarch will act only with the advice and consent of the Prime Minister and the cabinet makes monarchy compatible with a system of parliamentary democracy.
The system of monarchy contrasts with republics, where the head of state is an individual either directly elected by the people or appointed by an elected state parliament.