The chemical reaction occurring at the silicon surface during dry oxidation is
Si + O2 ® SiO2 -----------------DRY OXIDATION
And for wet oxidation is
Si + 2H2O ® SiO2 + 2H2--------WET OXIDATION
Dry oxidation has a lower growth rate than wet oxidation although the oxide film quality is better than the wet oxide film. Therefore thin oxides such as screen oxide, pad oxide, and especially gate oxide normally use the dry oxidation process. Dry oxidation also results in a higher density oxide than that achieved by wet oxide and so it has a higher breakdown voltage (5 to 10 MV/cm). 
In case of wet oxidation where water is use instead of oxygen, the water molecule can dissociate at high temperatures to form hydroxide OH that can diffuse in the silicon faster than molecular O2. Therefore the wet oxidation process has a significantly higher oxidation rate than the dry oxidation. It is used to grow thick oxides such as masking oxide, blanket field oxide, and the LOCOS oxide.