I was reading "What good is a volatility model?" by Engle and Patton on the train this morning. On the second page, they try to make a distinction between latent and stochastic vol. I don't quit get it. Could this just be professor-ways of saying "I am better than most people"? Then, again I am not too familiar with econometrics terms. Someone help, please!

I don't know the paper but "latent" is an econometrics term for a variable that appears in our model but we cannot observe, stochastic (in this context) probably just means "varying."People have come to use "latent volatility" to mean the unobservable parameter of underlying price changes to distinguish it from some observable form of volatility, such as implied volatility. "Stochastic volatility" usually just means non-constant.I know of no sense in which you would choose between "latent" or "stochastic" volatility. You can have either, both or neither. Moreover, in the context of a volatility model volatility will always be stochastic and non-latent (the output of your model may be a latent input to another model, but the dependent variable of your model cannot be latent).