According to the docker-compose reference,

Ports is defined as:

Expose ports. Either specify both ports (HOST:CONTAINER), or just the container port (a random host port will be chosen).

• Ports mentioned in docker-compose.yml will be shared among different services started by the docker-compose.
• Ports will be exposed to the host machine to a random port or a given port.

My docker-compose.yml looks like:

mysql:  image: mysql:5.7  ports:    - "3306"

If I do docker-compose ps, it will look like:

  Name                     Command               State            Ports-------------------------------------------------------------------------------------  mysql_1       docker-entrypoint.sh mysqld      Up      0.0.0.0:32769->3306/tcp

Expose is defined as:

Expose ports without publishing them to the host machine - they’ll only be accessible to linked services. Only the internal port can be specified.

Ports are not exposed to host machines, only exposed to other services.

mysql:  image: mysql:5.7  expose:    - "3306"

If I do docker-compose ps, it will look like:

  Name                  Command             State    Ports--------------------------------------------------------------- mysql_1      docker-entrypoint.sh mysqld   Up      3306/tcp

Edit

In recent versions of Dockerfile, EXPOSE doesn't have any operational impact anymore, it is just informative. (see also)

ports:

1. Activates the container to listen for specified port(s) from the world outside of the docker(can be same host machine or a different machine) AND also accessible world inside docker.
2. More than one port can be specified (that's is why ports not port)

expose:

1. Activates container to listen for a specific port only from the world inside of docker AND not accessible world outside of the docker.
2. More than one port can be specified

PortsThis section is used to define the mapping between the host server and Docker container.

ports:   - 10005:80

It means the application running inside the container is exposed at port 80. But external system/entity cannot access it, so it need to be mapped to host server port.

Note: you have to open the host port 10005 and modify firewall rules to allow external entities to access the application.

They can use

http://{host IP}:10005

something like this

EXPOSEThis is exclusively used to define the port on which application is running inside the docker container.

You can define it in dockerfile as well. Generally, it is good and widely used practice to define EXPOSE inside dockerfile because very rarely anyone run them on other port than default 80 port