Public v Password v Private – Any clear distinction?

This is probably a dumb question, but reading the Codex and searching the forums have not resulted in a definite understanding so here goes:

Page and Post Visibility Options are: Public / Password / Private. In some of the codex ‘private’ refers to non-Search Engine accessible blogs, so I’m looking for a clear, and hopefully concise statement of how the visibility options work.

Am I correct in the following:
– Public : open access by all
– Password : access only to that page/post content based on uniquely assigned password (What about child pages of that page?)
– Private : access only to logged in users that have a role defined as allowing access to “Read Private Posts” (are there various levels of private? So admins read more than editors?) In most cases, these logged in users will also get access to the dash board / user profile update and some other back end access.

For other password access schemas the various password plug-ins need to be employed.

Have I got it right?

Thanks!