Park Ball was not really a Pokeball at first as you can't hack it in DPPt, it was just a PalPark animation.
DreamBall was exclusive to DreamWorld and DreamRadar.
SportsBall was exclusive to Bug Contest.
Safari Ball is the problematic one as it appears in Safari of Gen1, 3, 4 and Great Marsh.
If Let's Go Safari is like a PalPark for Pokemon Go they should at least use the ParkBall or the Safari Ball.