The 1987 series has Bubba as a stereotypical Dumb Muscle cave-duck who had a pet Triceratops named Tootsie in 1 million B.C. Since none of that is accurate, the reboot has Bubba reimagined as a Genius Bruiser from tens of thousands of years ago, who only encounters Tootsie through Time Travel shenanigans caused by Louie's latest scheme. The ending has him carve a certain hat from stone and uses his stick as a cane, revealing that he is the first McDuck.
Speaking of Tootsie, she is reimagined as completely wild, to correspond with the fact that non-avian dinosaurs did not live with early humans, and behaves more like a real Triceratops, although this makes her hostile towards Bubba and the main cast. Her lizard-like appearance from the original show has also been exchanged with that of a warm-blooded animal with erect legs and a raised tail, thanks to Jurassic Park popularizing the Dinosaur Renaissance.
Bombie the Zombie was heavily changed. In the original Carl Barks comics, Bombie was a creature summoned to get revenge on Scrooge McDuck for conning a group of African natives out of their land. Since Bombie and the natives were designed up as racist designs of savages, this would never fly at all. This goes the same with the reasoning for the summoning. When it was brought in for the reboot, Bombie was reimagined as a Solomon Grundy-like monstrosity who was created to forever chase and haunt whoever proclaimed themselves to be the richest person in the world. Scrooge has been keeping it at bay for years and now has a different target after the events of the previous episode. The Bombie's whole reason for doing so is to serve Humble Pie to their target, so it maintains the spirit of its predecessor in terms of serving as a form of penance though here for hubris and lack of humility.
Donald Duck's iconic temper tantrums in the original shorts and comics often were targeted at the triplets. However, given how it would provide bad vibes of Abusive Parent for modern audiences, his temper is treated differently. We learn Donald actually goes to therapy and said therapist reveals Donald's anger outbursts comes from being a Cosmic Plaything and no one understanding him... literally. When he took the boys in and went to therapy, he channeled that anger into protective instincts, his outbursts now the result of unbridled fury at anything that could harm his boys.
Said therapist, Neighbor J. Jones, was originally Donald's old Sitcom Arch-Nemesis. Here, he runs an anger management business called Good Neighbor Jones. His relationship with Donald is professional though still vitriolic (though namely because Donald has been late with payments, due to his disappearance) because, hey, it is Donald after all.
Most of the appearances of characters from other Disney Afternoon shows are changed around to fit in with this continuity (especially since most of them weren't in the same continuity to begin with).
Similarly, Darkwing Duck is only an old TV show in universe. Then the old actor goes nuts after becoming fed up with the Darker and Edgier reboot and turns into this continuity's counterpart of Negaduck, and the actor hired to replace him ends up becoming Darkwing for real (which is helped when several of Darkwing's TV show villains get zapped into the "real" world thanks to a device that can cross dimensions). F.O.W.L. and Steelbeak also become major recurring villains as the show goes on (it should be noted F.O.W.L. appeared in an episode of the 1987 DuckTales first, though their depiction here hews more to their portrayal in Darkwing Duck).
Goofy as he appeared in Goof Troop appears in an episode that serves as a parody of sitcoms; unlike everything else in the episode, he's real, and an old friend of Donald's from college. Photos in his wallet also indicate Max, PJ and Roxanne all exist in this continuity too.
Two of the Wuzzles, Rhinokey and Butterbear, appear as giant monsters created by a mystical artifact, the Stone of What Was.
The Gummi Bears (only referred to as the "Great Ones") existed far in the past, and one episode centers around a younger Scrooge and Mrs. Beakley attempting to prevent a F.O.W.L. agent from getting her hands on the Gummiberry Juice formula.
Finally, Manny the Headless Man-Horse ends up being this continuity's counterpart toGoliath, of all characters, down to being voiced by Keith David once again. (Gargoyles as it was would never have fit into either the original or reboot DuckTales given its own dense mythology and presence of humans, so turning a seemingly new and random character into an equivalent was likely the best they could do.)