Four meanings of volatility

Distinguish actual, historical, implied and forward volatility.

Actual volatility is the true (unobservable) instantaneous randomness of the asset; historical is a statistical estimate from past returns; implied is the value that makes a model price equal the market price; forward is the volatility implied for a future period. Forward volatility between $T_1$ and $T_2$ follows from implied variances: $\sigma_f^2=\frac{\sigma_2^2T_2-\sigma_1^2T_1}{T_2-T_1}$. They generally differ, and trading their differences is volatility trading.