The types of Poké Balls available in each game differ. The Poké Ball displayed in Pokémon HOME corresponds to the type of Poké Ball that was originally used to catch the Pokémon.
If a Pokémon in Pokémon HOME is inside a specific type of ball and that Pokémon is moved to a game where that type of ball cannot be acquired, then the ball will display as an ordinary Poké Ball or a Strange Ball, depending on the game title.
Note that any time you move your Pokémon back to Pokémon HOME, the type of Poké Ball it was originally caught in will be displayed, regardless of what it was changed to when moved to another game.
To convert back to the original Poké Ball type used to catch that Pokémon, simply move your Pokémon to Pokémon HOME again.