Bahamut's true epithet is The Dawn Wyrm. This is a contrast to his counterpart and consort brood-sister Tiamat, The Dusk Wyrm. Bahamut draws power from the Sun, hence his "flare" based skills (which draw ambient solar aether). Dreadwyrm is likely to be either 1) a name bestowed upon him by his foes at the time of the Allagan Empire, or 2) specifically refers to the primal Bahamut.

That said, Wyverns have 4 limbs: 2 hindlegs and 2 wings. Like a bird. A proper wyrm has 6 limbs: 2 hind legs, 2 forelegs and 2 wings, which Bahamut is.