The Pokémon Sword Expansion pass is for Pokémon Sword and not Shield. Vice versa is also true. If you buy one, you cannot play it on the other.
Nintendo Support added that if you simply purchase Expansion Pass in the game menu screen’s lower right banner, you will purchase the correct one in the eShop.
Unfortunately, as noted on the official support page, Nintendo is not giving refunds for mistaken purchases. The North American page clearly states, “We are unable to provide refunds or exchanges for mistaken purchases.”
Earlier this year, the official Japanese Pokémon site also warned players not to purchase the wrong expansion pass.
As Kotaku previously reported, Pokémon Sword and Shield’s expansion pass, The Isle of Armor, will see new pocket monsters and adventures when it’s released on June 17. Be sure you get the right one!