Mariam, if I were to draw a distinction between the two:
The Kanban Board establishes visibility into work items as they proceed through an existing workflow. This promotes transparency, effectively radiates information, and supports tracking of work items against set WIP limits.
The Kanban Methodology includes concepts like value streams, system flow, and beneficial metrics like Cumulative Flow and Cycle Time to improve efficiency and ability to deliver
Now, that is my take on it, but I am by no means an expert in Kanban. The bottom line though in my opinion is that neither are fully valuable without the other.
Those practices leverage a Kanban board for implementing the kanban strategy. You could see that as an approach for optimizing flow.
The Kanban Method refers to an approach that leverages Kanban Boards and similar practices to pursue evolutionary change from your current process towards a more flow-oriented process/system, with minimal up-front changes other than visualizing the flow and limiting WIP.
In the context of combining Scrum with Kanban we use the kanban strategy - our goal isn't to move away from Scrum - it is to still do Scrum and complement it with a kanban strategy.