2.4 Types of damage
To defeat enemies, the most common way is via Attribute-based attacks launched by your team members. The other ways would be direct-type of damage also known as “snipe”, this kind of damage are set amounts specified in the active skills and it’s dealt before runestones are dissolved, this can help you save 1 round for the record, or jump directly to the next boss health bar without losing your current buffs. Aside from Attribute damage there is also Non-Attribute damage which is not decreased by elemental resistance, but rather by enemy defense (if any).
The most simple way that you probably already know, just dissolving runestones and matching attribute monsters will launch attacks based, damage is based on combo count, number of Runesotnes dissolved, and additional effects, etc.
Combo affects the amount of total your monster total attack that will be used for damage calculation. For example, dissolving 5 combos with 1 single group of your monster attributes will make them launch damage equivalent to their base attack, in most leaders then that number will be multiplied by the team skills and leader skills. So yes, higher combo count does affect how much damage your team is making.
Combo EX and other effects
One of the most popular effects is additional combo damage, this comes from leader skills like the one from Circe active skill which increases the damage from 25% to 40%. Combo EX is a mechanic originally from the Greek Gods which adds variable additional combos separated from the main combo count for the damage part, but those are not taken in consideration for enemy combo shields
Most leaders have a specific way to dissolve the board in patterns, Runestones groups, or starting positions, or dissolving specific runestone types. by fulfilling those specific styles you are rewarded with more damage and better skydrop, so keep practicing. The most notable leaders for this example would be the Babylon Gods and Primal Greek Gods.