Some context around what type of files and system we're referring to might help, but many services these days have opted for a different solution of showing who can see items when they are shared (with avatars, or using text, etc.), as opposed to just text that says it's been shared. This gives the end user all of the information, both that it's shared and who it's shared with, so it tends to be a better solution when applicable. In the reverse case for non-shared items, the absence of those indicators communicates that it hasn't been shared, preventing you from having to use those terms you're pointing out issues with at all.
You see this design system being used when communicating sharing by most of the major players like Google, Amazon, Dropbox, etc. Here's an example from a Google Keep note of mine:
Also here's an example from Amazon.
As you see Amazon do in the example above, some sort of 'Share' or 'Invite' UI can be displayed in the space when it hasn't been shared which also serves as an indicator that it's not shared with anyone yet.
I think this has become the dominant design for sharing UI and users have come to understand it. As they use your system they'll learn and you can (and should) always help them with tooltips and such.
I hope this different way of approaching it is helpful, and i do agree with you about text labels being easily confusing.