If you read somebody's journal
Sharing is paused means their page is dark for now. The reason is theirs, and the page does not say what it is. Nothing is deleted on either side, and it comes back as it was. If you want to know more, ask them.
Paused by your sub means they have paused their keyholder. Until they resume, you can do nothing: no tasks, no change to their planned end and no terms.
If it is your journal
Sharing is part of Plus. If your Plus has ended, your shares and their switches are kept and come back the moment you have Plus again.
Or you may have paused your keyholder, or everyone, on Sharing. Resume is there, and only you can press it.