Actually there are three major type base oils. Paraffinic, Naphthenic, Aromatic. All oils contain aromatic and napthenic rings. Paraffinic oils have more saturated rings and long paraffinic side chains.
The main problem with the stability of oils, and the materials that they are compounded into, involves the presence of polars and aromatics. These compounds contain impurities like nitrogen, sulfur, or oxygen which are highly susceptible to oxidation and color degradation when exposed to UV light and/or heat. Highly refined paraffinic oils have the lowest proportion of polars and aromatics and the highest proportion of saturated chains, making them the most stabile oils.
Aromatic's have the lowest flash point, Naphthenic fall in the middle and Paraffinic have the highest flash point. The higher the flash point the better.
Paraffinic base oils are the most widely used in engine oils. Napthenic and Paraffinic are mostly used in other types of oil.