High- versus low-explosives are differentiated on the basis of the speed of the reaction front, specifically whether it is greater than or less than the speed of sound. One can imagine reactions which involve little or no internal redox chemistry (Loss of a carboxyl group as carbon dioxide is technically a redox reaction in that the carbon is going from +3 to +4), but which generate lots of gaseous products. Maybe azides fall into this category, but I have not looked into them in any depth. One could differentiate those from reactions involving nitro groups or peroxides, in which redox chemistry is important.
Perhaps one way to differentiate substances is whether or not bonds to oxygen are forming to new atoms in the balanced equation. This might differentiate nitro-type or peroxide-type reactions from a hypothetical reaction involving loss of carbon dioxide (or some other gas). The latter might (in the universe of possibilities) create much gas, but the oxygen atoms are staying bound to carbon.