Okay, first we need to talk about creativity. Creativity is about thinking up setting, plot, or character elements that make the story meaningfully different from others. The definitions below are roughly standard, and if you ignore them just because you want to be different, that is obfuscation, not creativity. You have made a setting that is slightly harder to understand, but unlike actual creativity you have not made a setting that functions any differently once it is understood (the same can be applied to calling your orcs "baal'gara" and having them be red-skinned, horned beastmen instead of green-skinned, tusked beastmen - they're still cannon fodder for the dark lord and the only thing your weird naming scheme and very slightly non-standard anatomy has added is confusion). If you want to buck the standard naming conventions because it would help you communicate a new idea, do so. If you want to buck the standard naming conventions because you want to have a new idea, don't. That is not how ideas work.
Dragons are four-legged, two-winged, intelligent, have breath weapons, and can use magic. There's a lot of room to play around with the number of legs and wings on this one. The core identity of the dragon is mostly in being intelligent and magical, and the specific magic powers aren't even standardized.
Drakes are four-legged, two-winged, unintelligent, have breath weapons, and cannot use magic. Again, exact number of wings and legs and the presence of a breath weapon or not are pretty flexible. Being "like dragons, but not smart" is the defining feature, here. If your setting has both dragons and drakes, you can have the two of them look as similar or different to one another as you like, but dragons are smart and drakes are not. Now, the tradition of using "dragon" and "drake" to refer to the same creature goes straight back to Tolkien, and if you don't have unintelligent draconic creatures in your story it's fine to refer to an intelligent one as a drake, but only after you've already established that it's intelligent. This seems like nitpicking, but it can make the difference between the audience wondering or assuming the creature is unintelligent and the audience understanding both that the creature is intelligent and that both 'drake' and 'dragon' refer to the same thing in your setting.
Wyverns are two-legged, two-winged, unintelligent, do not have breath weapons, and cannot use magic.
Wyrms are dragons who are very old, or very powerful, or it is a very old term used to refer to dragons.
Serpent is a poetic word that can be used for any of the other creatures listed here or for regular snakes. Literally it means a snake, but calling a dragon a snake falls within poetic license.
Eastern dragons have no wings but can fly anyway, some number of fairly short limbs, are intelligent, and do not have breath weapons. You can call them lung (with italics to let readers know it's imported from Chinese and not the organ you use to breathe) if you also have western dragons and need to easily distinguish the two.