Q. Are two Abilities that are prefaced by the same text (before parenthesis) the same Ability?
A. No. Abilities such as Demise (Eternal) and Demise (Dead Horse) are two separate Abilities and can both affect a model at a single time. There are some effects that specify Demise Abilities, which affect all abilities prefaced by Demise.
Q. If a model declares the Onslaught Trigger during the same Action where its target declares the Regret Trigger, does the model still get to take the Attack generated by Onslaught?
A. Yes. Regret ends Step 2 (Taking Actions) of the Activation Phase and forces the model into Step 3 (End Activation).