AWS Fargate is a service that provisions serverless compute resources to run AWS ECS and EKS containers.  AWS states that Fargate allows you to focus on building your applications when you let Fargate provision and manage the infrastructure required. Think of it as containers on-demand with no underlying manually created infrastructure that are quick to launch and scale, where you manage everything at the container level.

AWS Lambda is a service that allows you to run code and containers without the need to set up, manage or provision servers. Lambda runs your code on highly available compute cloud infrastructure via Functions.  Lambda takes care of server and OS maintenance, scaling, code monitoring and activity/error logging.