Skyrim "dragons" are not true dragons by the standards of our real-world universe. They're technically wyverns if we're talking about how they are built, with wings built into their front arms like bats. HOWEVER, they are beings that only appear in the realm of Tamriel and - to our knowledge - what we consider a true dragon has never existed on Nirn. Plus, the dragons found on Nirn are intelligent. Every single one of them has the voice (lol) and a personality (if Bethesda bothered coding all of them). Parthurnaax (pictured above) wants peace and to stop the attack on humankind by his eldest brother, Alduin. However, he recognizes that domination is every dragon's natural instinct, so he feels that he should not intervene.
You can also see that Durnehviir in the Soul Cairn has a personality. We don't know a whole lot about him, but the overlords of the plain use his innate instinct to dominate to force other beings in the plane to behave. He longs to feel the light of Nirn on his scales again and asks for the player's help after he is defeated. I feel that this cognitive ability is what makes the biggest difference between a wyvern and a dragon. Plus, the world of Nirn is an entirely separate thing from our world, so their nomenclature is likely to have a few differences.
Outside of the world of Nirn, the difference between a dragon and a wyvern can be most clearly seen in worlds akin to the Witcher. I've been playing Witcher 3 some and found out that Witchers are bound by their code to not kill dragons, as they are sentient creatures. Wyverns, on the other hand, are fair game and I've killed at least one. There are so many other dracanoids in that game that it's an entire category in the beastiary and there is a specific blade oil for their kind. Shockingly enough, I have never watched Game of Thrones, as I find it too grim and focused on people. I don't care about literally anyone else but the dragons, so take the kingdom politics elsewhere please. I have enough politics thrown in my face as an American.