The difference between the two terms (sabot and driving-band) is related to their use during different time periods in artillery history.
As Scottfromgeorgia mentioned, the word "sabot" is French for a wooden shoe. It was one of many French words which during the Colonial era got adopted by the military services of European nations as names for parts of weapons and parts of fortifications. (For example, chevaux de frise.)
in the Smoothbore-cannons-only era of artillery (Colonial era through early-1800s), sabot meant the strapped-on wooden cup which held a cannonball to keep its fuzehole facing "outward" away from the propellant powder charge, and somewhat later, to allow a propellant powder-bag to be attached to the projectile.
When cannons with a Rifled bore (firing a cylindrical projectile) came onto the scene, in the mid-1800s, the familiar term sabot was applied to the metal cup, disc, ring, or band which surrounded a cylindrical projectile's base (or body). That use of the artillery term "sabot" continued to the late-1800s, when the band form of sabot had proven to be superior to all the other forms of sabot. Because of that, the term "sabot" was (mostly) replaced by the more-descriptive term "driving-band."
Put very simply, driving-band is the 20th Century term for what we civil war artillery buffs would call a sabot.
For anybody here who doesn't already know... the photo below shows the (fired, and therefore having rifling-marks) copperbrass driving-band on a World War One US 3.8" Shrapnel shell (which we civil war buffs would call a Case-Shot shell, because it contains dozens of antipersonnel balls).
In recent decades, the old projectile term of "sabot" was revived, with its definition being closer to its original Colonial era meaning. Now, sabot means a non-metallic cup or sleeve which holds the projectile prior to and during firing, and (intentionally) drops off immediately after the projectile gets fired. In both small-arms and artillery, that type of ammunition is called a "sabot round." It is the state-of-the-art tank killing projectile, which the Americans used with devastating effect in the US-versus-Iraq wars.
Regards,
Pete