How does damaging Shields, then Health work for elemental bonuses?

Question

Using two Sniper Rifles using almost the exact same damage, I noticed Head Shots from my Shock rifle on Shielded targets deal significantly less damage than Fire shots to unshielded targets. 110k damage from the Fire sniper, 69k from the Shock weapon.

If damage were calculated only once and applied to damage and health, the shock weapon should have dealt more damage; Shock's bonus against Shields is 2.5 (1.0 against Flesh) while Fire's bonus against Flesh is 1.75.

So what's happening here? It seems only enough Shock damage is dealt to take down the shields using the 2.5 calculation, then the remaining damage is dealt as if it was Flesh damage using the 1.0 calculation. Is any damage overkilling the shield, thus losing damage to the Flesh target or is only just barely enough damage dealt as Shield damage?

Is this calculation the same for other elemental types? For example explosive does 0.8 damage against Shields but 1.0 against Flesh; will the 1.0 multiplier be applied to Health "overflow" damage?

Answer 1

Damage is first calculated from shields, then the remaining damage is calculated by health.

For example you are using shock sniper, your damage with the sniper is 1000 (including all the bonuses and modifiers) but the damage is further multiplied by it's effectiveness on shields x2 on normal and x2.5 on true vault hunter.

Assuming the target has 1000 health and 1000 shields, you only damage the shields, but not the health, since the damage multiplier applies only to the shield damage and not the health damage.

If the target would instead have only 500 shields, the shields would take 2000 or 2500 damage and the remaining 500 points of damage is subtracted from the health (Only 500 points of damage from 1000 is multiplied with the shock bonus, since the target has only 500 units of shields)

This same rule applies to all elemental damage.

The elemental damage coefficient multiplies the adjusted weapon damage following the formula below:

Final Damage = (Base + Skills + BA Rank + Class Mod + Relic) * (Gun Base) * (Elemental multiplier)

Answer 2

Shock damage takes more "Life" out of a shield, as explained by the game, where as Fire damage takes more out of the Health of an opponent, assuming they are not armored, which is also explained by the game. Armored people take more damage from Corrosive, like Hyperion Robots, and Slag just makes them take more damage, helpful in Co-Op.