Actually these are two very different things.
A projectile for a smooth bore gun can/shall have an obturating band and as a matter of course no driving band as such is not required.
While a driving band basically is an obturator as such and depending on design (more often seen with older designs) a driving band may have a special obturating section which is usually very fine and somewhat larger in diameter than the rest of the driving band.
Also means that an obturator is doing exactly what it says; it is sealing something. Not more and not less. Also obturators are usually less strong in design (see plastic material being used nowadays or if made of metal are just fine over diameter flanges attached to a projectile) as these do not take or transmit any force (unlike a driving band).
After all driving bands do transmit rotation taking it from the rifling of a barrel and relaying it to the projectile.
A good example are obturating bands on APFSDS and HEAT projectiles which are fired from rifled barrels. There they are made of plastic as just sealing is required and no spin forces are to be transmitted. As you know these are then not even fixed to the projectile and do rotate free on the projectile bodies so they do not even transmit the slightest spin to the projectiles as it is not wanted (in particular with HEAT projectiles).