The difference between Docker and Docker-compose is simple: docker commands are focused on only one container (or image) at once while docker-compose manage several containers docker.
An example of difference of docker and docker compose is when you run these commands:
docker ps (-a)
In Docker, docker ps displays every docker instance currently running in your environment. If you add the -a option, then you even have the stopped ones.
docker network ls docker-compose ps
In Docker Compose, the docker network ls list the networks and docker-compose ps displays all the containers once started with it (currently running or not).