Clips in Omny Studio have three different visibility settings: Public, Private and Unlisted.
Public means the clip is publicly viewable on Omny.fm, written to the RSS feed of any playlist it's been added to, indexed by search engines and can be shared or embedded on a website.
Private means the clip is only able to be viewed by users with access to your Omny Studio account.
Unlisted means the clip is not publicly viewable, but can be shared via the Omny.FM link, embedded in a website, or linked directly to the MP3, and is written to the RSS feed of any playlist it's been added to.
Note: if you add an Unlisted clip to a playlist it will be added to that playlist's RSS feed, and be visible in the playlist, and the directories (podcast apps) that the RSS feed has been submitted to.
If your clip is set to "Private", it will not be written to the RSS feed of any playlists it is added to. If the clip was previously available in podcast apps (by being set to Unlisted/Public and added to a playlist) and then made Private, it will no longer be playable in podcast apps, and will be removed from the podcast's listing in podcast apps*.
*How long this takes depends on the podcast app, and some apps will 'cache' the clip and it will still be playable after a clip is made Private, for more on this see here.)
To change a clip's privacy setting, click on the clip and scroll down to the section marked Publishing, as below. To schedule changes in Publishing state for a clip, see here.