Stablecoins have gained significant popularity recently, with their market cap rising to over $180 billion. However, recent events have raised concerns about their stability. In this paper, we classify stablecoins into four types based on the source and management of collateral and investigate the stability of each type under different conditions. We highlight each type's potential instabilities and underlying tradeoffs using agent-based simulations. The results emphasize the importance of carefully evaluating the origin of a stablecoin's collateral and its collateral management mechanism to ensure stability and minimize risks. Enhanced understanding of stablecoins should be informative to regulators, policymakers, and investors alike.