Setting permissions on the board level
By default, all newly created Boards and the projects inside them are visible to all team members.
You can change this visibility setting at the board level, either when creating a board, or when editing it's settings.
If a Board is set to "members only", then all of the projects inside this board will always be set to members only as well, and always limited to those board members.
If a project is moved into a board that is members only, it's visibility will be changed to only be visible to those who are able tot see this board.
If you want to manage who can see individual projects within a board, be sure that the board is set to be visible to "Everybody". This will enable the visibility options on the individual projects within that board.