If zazen is when you’re on the cushion, and Zen is when you’re not, then the only substantial difference is whether you’re on the cushion or not. If zazen is what we call it when we’re on the cushion, then it doesn’t matter what we call it when we’re off. The key to zazen is if done with Right Intention, the difference between standing and sitting, i.e. between being on the cushion and not, will become clear and empty. To that end, advocating zazen with Right Intention is at minimum and all it means to spread the Dharma.
The key to zazen is if pursued with Right Intention, the difference between standing/walking and sitting, i.e. between being on the cushion and not, will appear clear and empty. Thus Dogen says in the Genjokoan that when Dharma fills this whole body and mind we realize that something’s missing. Not only does this mean realizing our psycho-physical self is empty, but that emptiness is form, and that when we have psycho-physical form it’s only finite, which means temporal and ontologically determined. To that end, we realize that standing is standing and sitting is sitting all because of this, which we already know is nothing special.