A private website is only accessible by its owner and all its registered users (members). You can mark a website (branch) private in its branch settings.
If a website (branch) is open source, it means:
visitors can access it,
its source code is public, including its entire filesystem,
its Story is public (list of commits, or saved snapshots),
anyone can fork it (clone it),
if it's a package, anyone can install it on their own websites.
You can mark a website (branch) open source in its branch settings.
A tool is a website (branch) that can access other websites. Originally, there was the IDE and some other websites that contained applications to edit other websites. Hence they were used like a hammer: a tool. They were not ends in themselves, they were only useful to edit other sites. That name stuck around for now.
You can mark a website (branch) as a tool in the branch settings.
Boomla supports sharing entire accounts, website groups or branches with others for collaborative editing. This feature was rolled out 2020-01-17 and there is no user interface yet for configuring that. Please shoot an email to set it up for you.
This is a fine grained access control mechanism with various roles. Each role defines what permissions it has, like making the website open source. Let me know if you need a non-admin level role.