The correct answer is Amazon ECS. This service is specifically designed for running and managing Docker containers at scale. Amazon ECS (Elastic Container Service) allows you to easily deploy, manage, and scale containerized applications using Docker. It integrates seamlessly with other AWS services and offers features such as task definitions, which specify how Docker containers should run, and service management, which helps in maintaining the desired state of your application.
While AWS Fargate is a technology that works with Amazon ECS and Amazon EKS to run containers without managing servers or clusters, it is primarily focused on the compute layer rather than being a comprehensive container management service. On the other hand, Amazon EKS (Elastic Kubernetes Service) is geared towards managing Kubernetes clusters, which can also run Docker containers but involves a steeper learning curve compared to ECS. Lastly, Amazon Lightsail is designed for simple cloud applications and does not primarily focus on container orchestration or management.
Therefore, choosing Amazon ECS directly addresses the requirement of simplifying the deployment and management of Docker applications.