Boarders are residents in a boarding house or school paying for their room and board (food), fighters who board ships, or more recently, people who go snowboarding a lot. You can also board animals, though usually only people are called “boarders.” All of these have some connection with boards: hunks of wood (the planks of a table, the deck of a ship, a snowboard).
All uses having to do with boundaries and edges are spelled “border”: border collies, Doctors Without Borders, borderline disorders, border guard.
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