Dragon Gate is the first stage that Dragoneye gains. In this form, he gets engulfed with fire. He achieves this form after Grim kills his mother. Most call it the "Dragons Rage" but its Dragoneye unlocking the fist gate that is blocking his dragon aura, hence the name Dragon Gate.
Unleashed:
Power levels are raised a bunch, increasing all the stats by 25%, (except speed which is raised by 50%), in gameplay, and MUCH more in cutscenes. It takes a lot of Aura though, so he can't maintain it for long.