What is the difference between add damage counters and attack damage
Damage:


Is affected by Weakness and Resistance, unless specified otherwise
Is affected by effects like "Whenever an attack does damage"
Can be prevented by "prevent all damage"
Can be reduced by "any damage done to this Pokémon by attacks is reduced by XX", "divide that damage in half", etc.


Damage counters:


Is prevented by "prevents all effects...", since placing damage counters is an effect of an attack.
And you can pretty much revert everything that applies to normal damage.