What makes a glowing splinter glow and a burning splinter burn
A splinter can undergo multiple types of thermal reactions depending on both the maximum temperature and amount of oxygen present.  The answer to the question seems to be in the difference between total and partial inceneration.

In total inceneration, which is very likely in the total oxygen atmosphere at high temperatures, all of the organic carbon is converted to carbon dioxide. Carbon dioxide is colorless so the emission of electrons, i.e. the glowing, is observable.

In partial inceneration, which occurs when oxygen is present but deficient, the organic carbon is converted into both carbon dioxide and a variety of volatile compounds observable as smoke. Smoke forms at lower temperatures than thermal emissions. Smoke can also obscure thermal emissions.