What I've concluded from reading several books and more importantly, asking for detailed information from a couple of RPing and Dragonic lore forums;
Dragons, Dragons are great variations of reptilian species with SIX appendages; four legs and two wings. They have a great variation of colour and shape(Read: Horns, claws, and skin) depending on habitat they live in. Depending on lore they may or may not be capable of breathing fire and/or other substances by means of magic or plain scientific reactions. Also notable is that dragons are often portrayed as either intelligent to the point of being sapient, or to the point of far outmatching other animals.
Drakes, Drakes as far as I've concluded are WINGLESS dragons(Which others above me have denied), smaller in size and less intelligent, albeit far from dumb. They also have a notably smoother skin and less colour variation. 160
Crudely explained they're big, reptilian dogs.
Wyverns, Wyverns are older variations of dragons, to the point of having less appendages(That is, the front pair of legs doubles as wings, sometimes with claws on the elbow), less intelligence, and inferior instincts. Most likely so because they're less evolved versions of dragons.
Wyrms, Wyrms are the most ancient version of dragons, most likely the whole race of dragons decended from this particular species. They cover a considerably bigger span of time than the previous three apparitions combined, explaining why their appearance ranges from giant worms to wormish-dragons. Wyrms are, as stated priorly, giant worms, with reptilian skin, and bigger, cruder faces, the eldest versions of wyrms don't even have horns. Wyrms are known for living underground. Later on they evolved wings and became sleeker in form; Chinese dragons are wyrms halfway trough evolving to Wyverns.
The evolutionary tree of these species goes like this: Wyrms -> Wyverns -> Dragons + Drakes
As you can see, drakes and dragons are familiars trough the wyvern, they have both evolved differently, explained by the evolutionary theory of <PERSON> to living in a different ecosystem, Drakes didn't have the need to either fly or breath fire).
So, there you have it, the history of draconic beings as far as I can conclude from different sources 376