Implied volatility needs to be annualized by scaling between time horizons, while the variance rate is an annual value by construction.

The variance rate scales with the square root of the holding period, while historical volatility scales linearly with time.

Historical volatility is less than implied volatility, while the variance rate is greater than historical volatility.

Historical volatility is calculated by taking the standard deviation of returns, while implied volatility is the volatility that equates the option price produced by the Black-Scholes-Merton model with the observed market price of the option.