(Actually K8s collection of Pods is usually a ReplicaSet, fronted by Deployment, from the perspective of making sure they run. The Deployment is related to a Service by labels and selectors, K8s service only decides what pods it will route traffic to. An ECS service is more like a Kubernetes deployment, and I guess what Kubernetes calls a Service, basically a load balancer, is just called a load balancer, and I guess you manage the ALB's configuration together somehow for your service group, manually or somehow other, or you can just create a new ELB each time, and pay again ...)
I had never heard of a Docker Service, but from the looks of it, the Deployment (or Task), Service, ReplicaSet and Pods are all rolled into one single abstraction, the "Service" in Docker Compose.