Pokémon Origins depicts the Pokémon Giovanni used against Red in his gym leader battle as being in Ultra Balls, which isn't a common sight in the main Animé.
(Said Ultra Balls have their current design, BTW).
Also, Pokémon Origins changed things a bit by having the Master Ball being in development by the time Team Rocket attacked it (IE, it existed only in prototypical form there), so Red didn't get one. (The Master Ball there's ALSO depicted in its current design as well!)
And the Animé changed the reason why Giovanni disbanded Team Rocket (he was reminded of having the same spirit that Red has), thus, having the events that revealed what happened to him in HeartGold/SoulSilver going through differently (perhaps having his encounter with Silver being an attempt to reconcile with him, but Silver still being afraid of him for the abuse, and, when he hears the radio broadcast, he wanted to go to the radio station, not to join up with them, but to stop them once and for all {but still perhaps challenge Ethan to test his skill as a Pokémon Trainer since he reminds him of Red} ).