What? The attack action is defined in the actions section of the PHB.
Another example: The Full Attack action is a full round action where you potentially make one or more attack rolls. The Charge action is a full round action where you potentially make an attack roll.
As I understand it, your contention is that the only thing that's important there is the distinction between "full round action" and "standard" or "frree" or "move" action. Since Full Attack and Charge are both full round actions, then when something says "While taking the Full Attack Action", they must be including Charge, right? It's the obvious consequence - the action type isn't clearly spelled out, after all.
So, with Whirlwind Attack, I can attack each creature within reach while taking the Full Attack Action. Since your logic agrees that it includes charging, I can move twice my speed and then make one attack on each creature in reach with a +2 bonus and a -2 penalty to AC. I had to give up my regular Charge attack to do it, but WWA says nothing about giving up my movement!
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... or, I could accept that there is more distinction between actions than just full round, standard, move, and free. The Full Attack Action is a full round action, and the Charge Action is a full round action, but that doesn't mean that a Charge is the Full Attack Action.
The Attack Action is a standard action, and Manyshot is a standard action, but using Manyshot is not the Attack Action.
-Hyp.