So I get it, you can't cleave and vital strike in the same round. My question then is why did Paizo use the term "attack action" in the Vital Strike description instead of the term "Standard Action". Seems like that would have avoided confusion.
I know that there are other things you can do as a Standard Action besides attack. But the description of cleave uses the phrase "As a standard action", not "As an attack action" like in Vital Strike.
Can an attack action be something other than a standard action?
The Attack action is a specific Standard Action. So that's a NO on your question.
It's not the only attack that's an action, but it is the only action that is "The Attack action".