Understanding how Docker volumes work with compose
db_data:/var/lib/mysql simply means that the db_data volume that was previously created will be made available in the container at /var/lib/mysql.

In you example it's created at the very end of the compose file.
From the Docker documentation: "The docker volume db_data persists any updates made by Wordpress to the database."

Compose volumes works the same way as the Docker engine.

In you case db_data is just a named volume instead of a path like your second example.