Short Answer 
Oligarchy is a political system where a small group holds power over the broader population, while aristocracy is a specific type of oligarchy defined by rule from elite, often noble, bloodlines. The main distinction is that oligarchy can stem from various powerful groups, whereas aristocracy is strictly linked to hereditary status.
Step 1: Understand the Concept of Oligarchy
The term oligarchy refers to a political system where a small group of people holds power and makes decisions for the larger population. These individuals often possess wealth, social status, or military control. Oligarchy can emerge in various contexts, including governments, corporations, or organizations where a select few dominate.
Step 2: Explore the Definition of Aristocracy
Aristocracy is a specific type of oligarchy characterized by rule by the elite or privileged class, typically linked to royal or noble bloodlines. Aristocrats often inherit their status and influence over governance. This system emphasizes a hierarchy where only those deemed worthy by lineage participate in ruling.
Step 3: Differentiate between Oligarchy and Aristocracy
While both oligarchy and aristocracy involve control by a small group, the key difference lies in their foundations. Oligarchy can consist of any group with power without the necessity of noble lineage, whereas aristocracy explicitly ties its rulers to royal families. This distinction can affect how authority and legitimacy are viewed in each system.