Swarm is a service that sits between your docker cli and your docker engines. It makes it as if you are talking to one docker engine from the cli when in fact you are talking to many. This makes it easier to manage docker engines across multiple hosts.
Compose is a tool that issues commands to docker engines and will e.g. spin up containers and link them together in the right order. It makes rote docker commands a little less painful. It can talk to a single engine or, apparently, many engines via Swarm.
When it comes to putting providing a production "service" based on containers you need to be able to add and remove docker engines, to, for example, deploy new code via rolling update. Google Container Engine (GKE) and Amazon ECS marry docker concepts with front-to-back implementations of hosted infrastructure like server instances and network load balancers. Over-simplified, each has an agent that runs on a docker engine and does work similar to Compose and Swarm against AWS and GCE. Google's daemon is called Kubernetes.