We usually use the word honing for just the finer stones. And some use the term grinding for both abrading with a coarse wheel and abrading with a flat,coarse stone. I usually start with an 800 grit stone and would not call this honing. Toshio Odate says to start with a 1200 stone and if that is not sufficient, the tool has gotten too dull.
I keep the tool about thirty degrees from perpendicular to the long edge of the stone, and sharpen in a back and forth motion. This is a very common technique, both in Western and Eastern practice. Introducing this angle makes the iron much more stable and less inclined to rock in the direction of travel. It is as if you have a much wider bevel to rest on. Being able to overhang the edge of the stone with the tool is important for both maintaining the flatness of the stone and for adjusting the camber of the blade.