Great question. The terms Backlog Item (PBI), User Story, and Task are often used in different ways and that can be confusing.
The simple answer to your question is that on a Kanban board (especially outside of Scrum) you usually have one level of item that may be user stories, tasks, tickets, requests, or whatever your team needs. So, if you want to generalize these things to "Tasks" instead of trying to use user stories, there is nothing wrong with that. For that matter, you can even use a mix of different types of items - they're just all on the same level.
With the simple answer out of the way, here's a little more complexity:
In scrum we commonly see two levels on the board: Backlog items and tasks. The reason is that it lets us distinguish between the value-add item (the backlog item - often a user story) and the discrete small thing to be done which is just a step in delivering the larger item. This is because, in scrum, we want to use the board for the team to organize their work (tasks) but also keep an eye on how the team is progressing toward adding valuable functionality to the product and achieving the sprint goal (PBI).
In a purely Kanban board, I'm just concerned about the flow of work, so there usually aren't multiple levels of tasks. In most cases, everything in a Kanban board is value-adding and the steps to deliver it come out in the columns of the board.