An API management system is a set of processes, policies, principles, and practices that allow owners to control their APIs, whereas an API gateway is a component or tool used as part of an API management approach. An API gateway acts as a proxy for incoming requests, facilitating tasks like authorization, rate limiting, and aggregating results. It provides a layer of abstraction on top of APIs or microservices, allowing developers and managers to reduce redundant tasks across all the APIs and perform them in one place. The key difference between an API management system and an API gateway lies in their scope and functionality, with API management focusing on the overall processes and practices, while an API gateway focuses specifically on managing incoming requests and facilitating tasks related to security, analytics, and logging.