The definition of BFC in the glossary says

Often used to refer to a block formatting context root, that is, a block box that establishes a new block formatting context for its contents.

Correct me if I'm wrong, but I think a BFC root is just a box that establishes a BFC. It's not necessary block-level, so it may not be a block box. For example an inline-block is an inline-level BFC root.

Instead of "block box" I would say "block container" or just "box".