next lichen
If you change manager, then you are moving, but often your tasks stay with your current manager.
In many orgs, it is not up to you decide which manager should be responsible for the tasks you are doing. That is often under the umbrella of organization design and based on agreements made between managers and their managers.
Some orgs can have more dynamic, bottom-up org design processes where people can suggest moving things around.
Be mindful about what is usual in your org before starting a discussion about moving your work from one manager to the other.