What decides whether a reaction releases light or heat
The amount of energy released by a reaction is what most often creates light. Burning, the energetic reaction usually caused by oxidation of something, creates light because the amount of heat released is large enough to heat the reactants or products to temperatures where the radiation emitted contains a lot of visible light (coals in a fire glow red because they are hot enough that black-body radiation has a significant component in the visible).

Most exothermic chemical reactions don't generate this amount of heat and, although they release heat, you don't see it. Hand warming pads, for example, often contain supercooled sodium acetate which can be made to crystallise by popping a small metal insert. The exothermic reaction (crystallisation) releases heat to warm your hands, but not enough to see visible light.

A very small class of chemical reactions produce light directly as the reaction leaves molecules in an excited state which decays with the emission of visible light. Glow sticks are an example of this. 

Overall, though, most reactions produce heat because the products have lower energy than the reactants and the released energy has to go somewhere. And it usually just ends up as heat. No photons are usually involved as the energy passes directly into the vibrational and translational energy of the products. So the excess energy in the reactants' bonds ends up as vibrational or translational energy in the products.