Rubbing alcohol means that it is alcohol that is meant to be applied topically (on the skin). It has nothing to do with the chemical composition of the compound. You can find/buy "rubbing alcohol" that is ethanol based. Most rubbing alcohols are based on isopropyl alcohol probably because it's cheaper.
Denatured means that the alcohol is unfit for ingestion. Some alcohols like methanol (aka wood alcohol) are "naturally" denatured because of their toxicity. Isopropyl isn't nearly as toxic and has additives to make it less appealing. Ethanol is what is in liqueur and it has the most additives to a) render it less appealing and b) to get an exemption from the drinking tax ;-)
The ratio of alcohol to water in % or proof (%/2) affects the flammability. 91% is extremely flammable and even the 70% stuff has a low flash point, 70 degrees. 91% only drops that down to 63 degrees.
