Both are oxidation reactions. Burning is just a lot faster than rusting.
Oxygen and Hydrogen would most likely form a covalent bond that is polar, or a polar covalent bond. Due to the electronegativity difference between the 2 elements, unequal sharing of the valence electrons will occur, electrons being in closer proximity to Oxygen and farther away from Hydrogen. Resulting in the characteristic partial positive and negative charges to appear for the respective elements.
D & e represent the same element
