TL;DR
What are the pillars of Kanban process? Are they the same [as Scrum] or is something different?
Kanban doesn't define "pillars" in the same sense as Scrum. However, as one of the core agile methodologies, it espouses a set of rules and principles that do map to the same agile objectives. The current set of six practices (described below) collectively map to the pillars you describe.
The Kanban Method
However, David Anderson's Kanban Method describes the following four basic principles:
- Start with existing process
- Agree to pursue incremental, evolutionary change
- Respect the current process, roles, responsibilities and titles
- Leadership at all levels
Kanban, which grew out of manufacturing, describes the following rules for manufacturing:
- A later process tells an earlier process when new items are required.
- The earlier process produces what the later process needs.
- No items can be made or moved without a Kanban.
- Defects are not passed on to the next stage.
- The number of Kanbans is reduced carefully to lower inventories and to reveal problems.
— Mattias Skarin. Real-World Kanban (Kindle Locations 188-191). The Pragmatic Bookshelf, LLC.
Open Kanban
Open Kanban then defines four key practices:
- Visualize the workflow.
- Lead using a team approach.
- Reduce the Batch Size of your Efforts or Reduce BASE.
- Learn and improve continuously.
Within these practices, the Visualize the workflow and Learn and improve continuously principles provide the inspect-and-adapt cycle.
Kanban's Six Practices
It's worth noting that most practitioners now accept that there are six key practices:
- Visualize workflow.
- Limit Work-In-Progress (WIP).
- Manage flow.
- Make process policies explicit.
- Implement feedback loops.
- Improve collaboratively, evolve experimentally.
— Mattias Skarin. Real-World Kanban (Kindle Locations 195-206). The Pragmatic Bookshelf, LLC.
Here, there is a much clearer mapping to the Scrum process controls:
- Transparency
- Visualize workflow.
- Make processes explicit.
- Inspection
- Implement feedback looks.
- Evolve experimentally, because the exposition of this principle refers to the scientific method, which requires both measurements and observation.
- Adaptation
- Implement feedback loops.
- Improve collaboratively, evolve experimentally.
While it's not as simplistic as the "three pillars" in your question, and there is some complexity and overlap in the implementation, current Kanban practices do a good job of providing the same things, and can often be smoothly integrated within Scrum, Lean, or even XP implementations.