Hi Phebe,
Trello is moving to a model where you can think of Teams as “workspaces” and all boards will eventually be in a Workspace—be that a business workspace, a home workspace, a book club workspace, etc. There are a lot of small changes we need to make (and some big ones) to get there but you can imagine the end state as all boards are in a workspace (and a workspace is essentially what we call a Team today).
One of these changes is that from now on all new boards must be placed into a Team. That's why the option "No team" is not available anymore in the "Create Board" and "Move board" screens. You can choose from your existing teams or create a new one to hold your new board.
Even if you invite someone to join your team, you can still make your board's visibility private, making it only visible for the board members. If you never explicitly invite a user to a private board, they won't have access to it even if they are a member of the team that holds the board.
I hope this helps to clarify! Let us know if you have any other questions, and have a great rest of your day!
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