High and Low Side Driver vs. Half-Bridge Driver
The 2108 has "cross-conduction" (aka shoot-through) prevention logic - this means both FETs won't be driven at the same time and there will be a small dead-band. This makes them suitable for use on FETs on the same side of the H bridge.

The 2106 doesn't have this feature because it is suitable for FETs in opposite corners of the H bridge where they both need to be activated simultaneously.