@Myles stories belong to an actor (person, group, event, etc.) and displayed on their profile. Applications are installed on profiles and every application used by a profile (owned by that actor) can create automatic stories as the result of actions that happen on them.
For example when discussions app is installed on a profile, when I create a new topic or comment on a topic, new stories are created and displayed on the actor profile. Same when I upload images, create an album, publish a page, edit a page, etc. stories are generated and displayed in the profile.
The actor admins (or followers depending on the permissions set by the admin) can also post manual story updates right from the profile by entering their story update in the composer box on top of the story feed.
For example when you create a group you become the admin of the group. You can set the permissions of the group profile so the group's followers can also post story updates or you can keep that right exclusive to the group admins only. For a person profile the person is considered the admin of that profile.