In the World of Orea, it works like this: Dragons are...dragons. Wings, breath weapons, mostly speaking, several magic using [and/or psychic] chromatics, metallics, and mineral/crystal/gemstone.
Then there are the Dragonkin: Wyverns, Behir, Dragonnes (called Dralions or Ligons [tm], for copyright) and Hydra. These creatures can breed amongst themselves (if two ever find each other to do so) but most are born from chromatic dragon clutches. So you can have black-dragon behirs, red-dragon hydras (ye olde pyrohydra anyone?), etc... Pseudo-dragon-like critters (called "lapdrakes" [tm] in Orea) could also be considered dragonkin, but are usually viewed as their own species of dragon.
Drakes and linnorms exist in the world...I suppose...in theory (I would, actually, probably just combine them/make them different names for the same thing), I've just never had cause to use them. These, too, I would place as dragonkin, not full dragons themselves...missing wings or missing/lesser breath weapons or whatever that doesn't make them, quite, "dragons"...at least in the eyes of the sages of Flin [tm].
And there are exceptionally rare [on the Orean Prime] extra-planar dragons, collectively referred to as the "Celestial dragons", but including Shadow, Faerie -
these ain't your mama's butterfly-winged squirrel-sized dragon-pixies, as well as a species of "thought" dragons who can traverse most planes but reside/originate in the Astral.
WotC is perfectly welcome to hire me to organize, write and layout their MM.

[MENTION=42582]pemerton[/MENTION] Linnorms, traditionally in legend and as I understand them (and this might not be technically true of D&D linnorms), are simply 2- or 4- legged flightless (usually wingless) "dragons." Possibly with serpentine bodies. Possibly more clunky/thicker builds. Breath weapons are either absent or some kind of minor/small effect. But they are big, reptilian, dangerous "animals." No talky. No magicky.