The European dragon looks like a single ancient animal and is in fact an assembly, put together over roughly fifteen hundred years from parts with separate origins.
The oldest layer is verbal. Greek drakon means a large serpent and carries no implication of wings, legs or fire; it is used of the snake guarding the golden fleece and of the Python at Delphi. Latin draco inherits that sense. When Christian writers needed a word for the sea-monsters of Hebrew scripture and for the great serpent of Revelation, they used it, and a serpent of Greek natural history acquired a theological role.
The second layer is Germanic and is where the dragon gets most of what people now picture. The dragon of Beowulf lies on a hoard in a barrow for three hundred years, is roused when a cup is stolen, flies out at night and burns the countryside, and is killed by an old king who dies of the wound. Every element of the modern hoard-dragon is there: the treasure, the barrow, the thief, the fire, the fatal victory. Fafnir in the Norse material adds the theme of a man who becomes a dragon through greed.
The third layer is hagiographic and chivalric. Saints subdue dragons, Margaret, Michael, and above all George, whose dragon-slaying is a late medieval addition to a much older martyr's legend, and the dragon becomes the standard adversary against which a knight or a saint is measured. The four-legged winged body familiar from heraldry is a product of this period, not of antiquity.