The four states of matter are gas, liquid, solid, and plasma. Fusion produces plasma, the fourth state of matter. Oxygen is the catalyst in the exothermic reaction that produces fire and among its byproducts carbon dioxide (oxygen is not consumed in fire).
The structure of the sun is such that it has an iron mantle surrounded by a sea of plasma. What occurs inside is the fusion of hydrogen nuclei into helium nucei, four of hydrogen to produce one of helium. In a hydrogen bomb, a deuterium ion and a tritium ion, the positive isotopes of the heavy isotope of hydrogen, undergo fusion to form a helium nucleus and a neutron. The ideal fusion of two hydrogen atoms plus two neutrons to form one helium atom can not be reproduced. Find out the latest of what we know about the sun at this very hot site here...
http://www.thesurfaceofthesun.com Is fire plasma? Well, yes. So are electric arcs. Plasma has different densities that can make them appear to fall into different classes.