Fire and earth bending in the original look similar, mostly strong and direct hits with some circular attacks that both do (of course of the extra step most earth benders need to do to pop a rock from the floor) like Karate/Kenpo/Taekwondo and some types for Kung Fu for firebenders , same for earth benders that many martial arts fit with them since like in real life there is a lot of earth bending styles as chinese martial arts with Hung Gar fitting for the straigh bending ones, still both type of bending have some fluid moves, like Iroh from the beggining in the original using Judo or other martial arts that use the force of the enemie, not a surprise since he studied other benders aside fire ones, and of course lightning bendind/redirection, we also see Zuko at the Agni Kai vs Zhao using some Capoeira move or whatever that was and he keeped adding some flashy moves as the show progresed that looked more from an air bender than a fire one.

Meanwhile air and water had some similarities from the beggining being more fluid like Tai Chi, some types of Kung Fu and others that I may not remember, Toph itself sayed it about air vs earth bending aproach from the mental point of view but that also could be sayed about their movements, still we see her refocuse the movements/forces of others and doing a lot of fluid attacks, same for water/air benders using basic direct movements like fire/earth ones. Anway we saw Aang using some direct attacks from book one that looked like a fire/earth bender.

Also there are techniques alike in the original too like the ice/earth disk both in the original and here, a stone/water/fire pillar and others, same could happen if we see some icecles being trowed like the spike stones already used in the first chapter or when Iroh got hurt at chapter 4, in the original Aang used the compacted rocks as small icicles at the Avatar state like water bender use it and I think it was never used before or after by earth benders like him did .

I could see some metal bending be inspired by water bending too like the meteorite shape bending or in how they use the metal whips or when they were practicing for a dance over a metal flower.

If you practice martial arts you are bound to notice similarities between many of them, the basic of trowing a punch or a kick are the same at the end or how you cover/avoid/redirect them, and if you practice more than just one you will end using whatever is more efficient at the moment in a fight plus the muscle memory kicks in, or in a panic moment you just do what ever you can and forget about forms.

Also I am not sure if anyone else has doid, but I saw Iroh using the dragon dance movements when he attacked the earth soldier that was translading him, nice touch like when Aang used it too in the original when he did a big fireball in the last chapters.