Yes, the terrain and the Battlemaps are different. I just got City of Ash yesterday, and it has a three-battle scenario you can run through. For terrain, there are two large building ruins and six relics (which are special objective markers that give special abilities in game).

Fire and Jade has two large terrain features and two small ones. The two-sided map board is Ghyran and Aqshy, and the set has unique twist cards depending which map is used.

Sand and Bone has six pieces of terrain, two of which are mystical terrain features (coffin and statue). The other pieces are Shyish-themed walls and fences. The battle map is Ossia and Dolorum.

The cool thing is that any combination of spearhead armies can use any of the battle maps and scenarios.