The differnce lies in the time dependency of the SABR model parameters.
Suppose today is Nov 1,2008. You have 2 sets of options of different strikes expiring at maturity of Dec 1,2008 and Jan 1,2009.
In the static SABR model, we obtain 2 sets of SABR model parameters corresponding to the smile at each maturity. After completing calibration of static SABR we get 2 implied volatility smile curves.
Dynamic SABR is based on the same SDE as the static SABR, with the added feature that the SABR model parameters are time dependent. Hence after completing calibration of dynamic SABR model we obtain a continuous implied volatility surface
