In the free version, my understanding is that if a board is "private" only members of that specific board can view that board.
Q: If the board is on a workspace with various other boards, are members restricted to only those boards in the workspace to which they have been invited?
Thanks for writing to us!
You're right! In the free workspaces, you can set the board's privacy to private, so that only board members can access it.
Regarding your second question, if we are still talking about the free workspace, members will only be able to access the boards they have added, unless the board visibility is Public or Workspace Visible, which means that all Workspace members could view it, even if they are not members of the board itself.
If you are looking for more control and features, you can upgrade your Workspace to Trello Premium, which adds several features to make managing teams a bit easier, including the ability for Workspace administrators to take control of all boards in the Workspace.
I hope this helps clarify your questions.
The Trello Team