Taken from Japan-tool's website. Maybe this explains what I mean.
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Ahhh, I think we're using "grain" to talk about two different things.
There is the layers--like stacked paper. All of the Japanese hones are cut the same way in regards to those--the layers are on the sides. Notice that So says "Not the cross grain side like in finishing hones." Finishing hones are not flattened on the cross-grained layers.
There is also "grain" in reference to the arrangement of the particles within the layers themselves. They follow subtle lines--if you look at the direction of cracks/lines on the surface of the hone, you will find that in a finishing hone, they will fall across the hone. I think that's what So is referencing.
I'm not sure now Jim but I know he told me I should hone on the narrow side of my Aoto which I bought from a certain 'infamous' :p eBay seller who will remain nameless.
On my one the layers appear longitudinal on the 'right side' The other side was crumbly & wrecked my edges.