is a specific kind of: bog plant, marsh plant, swamp plant.

is a broader term that covers: bullrush, bulrush, cat's-tail, nailrod, reed mace, reedmace, Typha latifolia | lesser bullrush, narrow-leaf cattail, narrow-leaved reedmace, soft flag, Typha angustifolia.

is a member of: genus Typha, Typha.