My mental model of a Docker image is "the environment in which a given application runs", from the application's perspective, it has the entire machine to itself.
My mental model of a service is a single entry point ("address") that dispatches incoming service requests to one of N different processes. Each process is running inside a Docker container.
A process is an program, running inside a Docker container. A process has 0 to N service dependencies, and connects to these services by way of their addresses.