Kenny Omega was the cleaner, he was heavily involved in Bullet Club interference at the start and slowly turned face as the Best Bout Machine, his gimmick basically becoming that he was way too good and exciting a wrestler to be a heel, kind of similar to modern Ospreay, though he was never as big a cunt as Ospreay consistently is. He had gay elite storyline bullshit no one with taste liked.
Jay White is a pure classic heel with an added focus on counter wrestling. He's a piece of shit and he makes it part of his gimmick that he's actually genuinely mentally unwell, rather than just making silly faces like Kenny Omega did. He's much more promo focused and talented than any other Bullet Club leader and his matches are also more of a classic style of wrestling with the added "OUTTA NOWHERE" element that is not nearly as prevalent in any of the other Bullet Club leaders thanks to the inventive Complete Shot and Blade Runner counters. His entire run, he cheated severely and never made the face transition (though he hinted at it) and he always has moments where he does low blows or Gedo interference somewhere in the middle of the match for the sake of heat, though it is true that, aside from some places early in his run, he always won through sheer talent by the end.
David Finlay is early on and he has some loose Jay White similarities, but he very much stands as his own man overall, and in fact, if I had to pick someone to be the closest approximate, it'd be Prince Devitt himself. He wrestles a slightly more Junior style but loves brawling and duking it out (Jay White fucking hated doing fighting spirit exchanges 99% of the time, Finlay loves them). On top of that, so far he's the only Bullet Club leader that has never had to cheat to win, though who knows if Gedo intends on that continuing to be the case forever. Right now he's proving himself by just going on straight up brawls and luving to fight, Maggle.
The copycat accusations are overblown and uninformed.