difference between "attack damage" and "damage from attack skills"?

I have noticed this difference in wording multiple times now. I'm curious whether these stats are just arbitrary differences in wording or have actual mechanical difference.

The only possibility I have come up with is that plain "attack damage" only affects the hit and not DoT nor secondary damage (which I know to be a fact), and damage from attack skills actually affects all parts of the damage.

This Idea is consistent with other passives on the tree. For example, there are passives, which grant X% damage to hits and ailments with [some weapon]. This makes sense as ailments are always a result of a hit (afaik?), but then there are other passives which need to grant damage to DoT outside of ailments, and can't do so with the "attack damage" archetype, since the dot is not a result of attack damage, and therefore have to resort to a description which doesn't limit itself to the hit of a skill, but to the skill in general, as seen in ["12% increased damage with bows" and "12% increased damage over time with bow skills"].
This also implies that ["12% increased damage with attack skills while fortified"] in the champion ascendancy scales, for example, Caustic Arrow DoT and various secondary damage with attack skills.

Can someone confirm this?

Im not sure but i think its the difference between outgoing and receiving damage after mitigation.

ok. Just realized I could just test it in PoB. According to PoB it behaves exactly as I hypothesized.

(1) "bow attacks deal x% increased damage with hits and ailments" doesn't apply to any damage over time from non-ailments.
(2) "%increased attack damage with bows" doesn't apply to any DoT.
(3) "%increased damage from bow skills" applies to all portions of damage.
(4) "%increased damage over time from bow skills" applies solely to damage over time from bow skills (this includes ailments).

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mlemmery wrote:

(2) "%increased attack damage with bows" doesn't apply to any DoT.

Adding here that the actual descriptions in the game are worse than yours. It says "increased damage with bows" not as you say "increased attack damage with bows". This is IMO impossible to understand without knowing or guessing how it works.

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Zrevnur wrote:

It says "increased damage with bows" not as you say "increased attack damage with bows".

True.