From what I understand our sun doesn't actually "burn", instead a nuclear reaction is taking place, which is the cause of heat, light and a electromagnetic radiation. I believe this is called Hydrogen fusion.
My question, is there another gas that could fuse in a similar way - at the same, or similar rate - or is Hydrogen unique in this regard?
Hydrogen is the easiest element to get started "burning" into helium via nuclear fusion. Helium will "burn" too via fusion but is harder to "ignite". Each successive element as you go up in mass in the periodic table is capable of supporting fusion but as the mass goes up, the temperature needed to trigger fusion increases while at the same time the amount of energy release goes down until you get to iron, at which point further fusion "burning" absorbs energy instead of releasing it.
There's plenty of helium in our sun but the temperature at its core (where fusion takes place) isn't high enough to fuse helium into anything heavier. This means that to fuse stuff heavier than hydrogen, the star has to be bigger and heavier than our sun. The biggest stars (like blue supergiants) can "burn" hydrogen all the way to iron.
