The term "block container" is misleading. CSS 2.1 defines it as

A block container box either contains only block-level boxes or establishes an inline formatting context and thus contains only inline-level boxes.

However, the name seems to suggest that it can only contain block-level boxes. Probably, that's why CSS Display wrongly (#1185) defines it as

A box whose contents participate in a block formatting context.

So maybe the notation should change. Something like

• flow container: either a block container or an inline formatting context root.
• block container: a box whose contents participate in a block formatting context. [...]
• inline formatting context root: box that establishes a new inline formatting context for its contents.
• block box: a block-level box that is also a flow container.
• <display-inside>: flow: If its outer display [...]. Otherwise it generates a flow container box. [...] It either establishes a new block or inline formatting context for its contents, or integrates its contents into its parent formatting context.
• <display-inside>: flow-root: The element generates a flow container box [...]. It always establishes a new block formatting context for its contents.

This would be more consistent with the flow and flow-root keywords.