There are several visibility options:
Public: The clip is accessed with an Omny.fm link (will appear in the show listing and will be indexed by search engines), can be embedded, can be downloaded directly, and will appear in RSS feeds if added to a playlist.
Private: The clip is not publicly visible or accessible. Cannot be added to a playlist (RSS feed) but can be scheduled.
Unlisted: The clip is not publicly viewable (and should not indexed by search engines), but can be shared via the Omny.fm link, embedded in a website, or linked directly, and will appear in RSS feeds if added to a playlist.
Note: If you add an unlisted clip to a playlist, it will become visible in the playlist (and its RSS feed), for more on visibility please see this guide.
When creating a new clip via the Clip UI, the clip will by default be set to Private.
When creating a new clip via the Playlist UI, the clip will be set to the same publish state as the playlist, i.e.
if the playlist is Private, clip will default to Private
if the playlist is Public, clip will default to Public