Although it’s not officially confirmed, it’s highly presumed that they are based on the same design

Oh I have no doubt they're based on the same design, but in my opinion it's like comparing Brock from the Anime to Brock from the games. Same person but from a different media/universe. Take Red for example. His RBY counterpart doesn't look at all like his FRLG version. They're still technically the same person with the same role, but with Pokémon's multiverse universes, they would technically not be considered the same person. Take Archie from Team Aqua as an example. Are they the same person with the same role in RS vs ORAS? Yes and no at the same time. He's got a totally different design while still being the same at the end of the day. It doesn't matter much because they're counterparts of each others, so even if it's just a costume change and not a new Green character, it remains the same as if they decided to give another version of Red his original black longer hair design from RBY.