In Kanban there is no task board. The visualise the workflow principle suggests to so the current state of the work items, which can be user requests, bugs, features or user stories. Moreover, in Kanban you don't visualise a team's work, but the whole organisation. Here is an example:
Additionally, Kanban should visualize the whole process, because this is the place where it can help the most. Don’t get me wrong, it is also fine to have Kanban on the team level, but the real optimization and improvement should happen on the highest possible level.
A more interesting fact, that there is no Kanban board at Toyota. They use a Heijunka board which looks similar to our Kanban boards, but it is used for signalling: knowing that something is wrong or can be improved.
The boards in different Lean/Agile/Kanban approaches look the same, but their purpose is different (Agile: tracking, Lean: signalling, Kanban: improving). Therefore if you look at a certain board, it is good to know which method the owner of the board is using.