Parabuzzies are Para-Beetles with a retranslated name and applied RPG physics
Para-Beetles are winged Buzzy Beetles appearing only in platformers, and Parabuzzies are winged Buzzy Beetles appearing only in RPGs. The primary difference between them is that the latter has legs, making it a simple "winged Buzzy Beetle", while the former doesn't, supposedly making it a seperate species.
"Parabuzzies have legs, Para-Beetles don't."
Most likely, the reason for Para-Beetles not having legs is because of sprite limitations during the NES era (as legs would not fit on the sprite in the first place). As for Para-Beetles not having legs in later games, that's probably because they wanted to use a familiar design, not to mention that Para-Beetles don't need legs, as they don't lose their wings when jumped on.
"Parabuzzies lose their wings when jumped on, Para-Beetles don't."
Parabuzzies most likely only lose their wings when jumped on for consistency, as other "winged X" enemies in the Paper Mario series (such as Paragoombas or Paratroopas) do. This is also why they have legs, as it would be odd if they suddenly grew legs when jumped on.
"They could've made them act like platforms on the overworld."
The Paper Mario series has the tendency to change enemies a bit to fit the genre more, even if this means making them killable in ways they normally aren't. In fact, let's look at the Bill Blaster example for a second. In almost every game, Bill Blasters "act like platforms on the overworld". But because that doesn't translate well into RPGs, they were changed into actual enemies for most of the Paper Mario series.
They even have slightly different designs than normal (being forward-facing instead of double-ended). In fact, Sticker Star could even be used as evidence to split Paper Mario Bill Blasters from "normal" ones, seeing as how that game uses the standard design and makes them overworld hazards instead of enemies. Honestly, Paper Mario Bill Blasters probably would be split if they were retranslated as "Bullet Blasters" or something. And Parabuzzies would almost certainly be considered Para-Beetles if they were translated just slightly differently.
"Parabuzzies actually attack, Para-Beetles are harmless."
Para-Beetles do contact damage, which is pretty standard for platformers. As for going from only doing contact damage to having an actual attack, that happens all the time in RPGs.
"Para-Beetles have red shells unlike normal Buzzy Beetles, while Para-Beetles have "normal" shells."
Spike Tops also have red shells in the platformers they appear in, but in the second and third Paper Mario games, they have blue shells like every other Buzzy Beetle. Red Spike Tops are even a seperate species in TTYD (and, judging by unused assets, Red Buzzy Beetles, Red Parabuzzies, and Red Spiky Parabuzzies were going to be as well).
"They have different names."
Only in English. They have the same name in every other language. And while I'm not going to ignore that people make mistakes, when English is the odd one out (like with TTYD's "Piranha Plant"), it starts to look more like NOA made a mistake, as opposed to literally everybody else.
Additionally, TTYD's localization was notably terrible. Besides the aforementioned "Piranha Plant", this is the same game that referred to Goomboss as the Chestnut King, and mistranslated "Paipo" as "Pipe".
"What is 'RPG physics' even supposed to mean?"
It basically refers to recurring enemies acting differently in RPGs than they normally do in platformers, due to the differing battle systems. One of the more common examples of this is Bill Blasters being treated as enemies instead of part of the scenery, or Lava Bubbles floating instead of jumping out of lava.
"Platformer-style Para-Beetles make a cameo on a fountain in TTYD."
Platformer-style Lava Bubbles appear in the Bowser segments in that game, as do normally-sized non-boss Bloopers. There's a difference between two species coexisting in the same game and a different design of a species appearing as a callback.
"If we're using the Japanese name as proof, should we merge Kamek and Magikoopa?"
Faulty argument, comparable to saying "If we're using the English name as proof, should we merge Yoshi (character) and Yoshi (species)?". Also, there's a decent amount of evidence for Kamek not being a seperate character, but that's offtopic.
"Super Mario Maker has Parabuzzies, and it's a platformer."
They've never been officially named. The only reason they're being considered Parabuzzies and not Para-Beetles is because they're visually "Buzzy Beetles + wings", and they keep their legs, making them Parabuzzies by the logic keeping them split in the first place. And to quote the Parabuzzy article:
In Super Mario Maker, if the player applies wings to a Buzzy Beetle, it will fly in a straight line and thus behave in a similar manner to Parabuzzies. Despite this, flying Buzzy Beetles cannot be stomped normally; they can instead be used as floating platforms, since the player can actually stand on their hard shells.
So if the main reason why Parabuzzies aren't Para-Beetles is that they look and act differently, then why doesn't this count as evidence they're the same thing? They have legs (which proves they're Parabuzzies), but they're platforms (which proves they're Para-Beetles).
"Those are just Buzzy Beetles with wings, they're never named."
It's pretty obvious what they're supposed to be. We're not going to consider Paragoombas in that game "Goombas + wings" or something, as there's already a clear equivalent. In this case, there's already a visual equivalent, and a behavioral equivalent.
Parabuzzies are most likely just renamed Para-Beetles in an RPG setting, similar to Podoboos/Lava Bubbles, and Super Mario Maker heavily supports this. Also, it's highly unlikely that every region got the name wrong except North America, which has been known for random renamings in the past.