What visibility changes
Visibility is set when a wiki is created and can be changed afterwards by its owner or an admin, through the settings screen or update_wiki. The tree of nodes and the MCP tools work the same way whichever value it holds; what differs is who can read the wiki and how it is reached.
Self-hosting is not one of those values but a way of running the engine, kept here because it answers the same question a reader is asking.
Public
Anyone reads, search engines index the content, invited authors write. SEO ships ready out of the box: no plugin, no external generator, no extra deploy step.
Private team
Invited members read and write; everyone else gets a 404. Hidden from search engines and from link unfurls. Suits project workspaces, internal documentation, in-progress drafts, and anything that should stay inside the team until it's ready, or stay there permanently.
A single page can be lifted out of that for a reader outside the team, through the read-only link share_page mints. The rest of the wiki stays invisible.
Self-hosted, single user
Runs on your own machine. Same engine, same MCP tools, no cloud dependency, no accounts: the bootstrapped user owns everything. Suits confidential data, offline work, and personal scratchpads before anything goes public.