It is at least the theory behind multifactor investing. It was initiated by Eugene Fama, the father of the Efficient Market Hypothesis. Several years after having formulated the EMH (and that the EMH was by then vastly taught in academia), Fama noticed that two sub-sets of the stock markets consistently beat the market : small caps, and value stocks.
Instead of just admitting that the EMH does not always work everywhere all the time, Fama concluded that, since these stocks consistently bring better returns, they must be riskier. As you can tell by now, I think this is nonsense, formulated by a guy who could have the heart to deny his cherished theory.
It is indeed nice, we can see how central banks policies progressively deteriorates the returns of asset classes.
Volatility, standard deviation and variance all refer to the same thing, with variance = (standard deviation)^2
However, as i said in my previous post, I strongly disagree with it being a good proxy for risk. Risk is permanent loss of capital, not the volatility of a stock.