Thank you to everyone for the thoughtful and detailed replies.
Here's a summary of gyaku
, as I understand it its usage at our dojo, after talking to my teacher, Dave Goldberg Sensei. (Emphasis and explanations here are my own mess.):
In ai hanmi
, partners stand with their same foot forward
(that is, both have their right foot forward, or both have their left foot forward).
In gyaku hanmi
, partners mirror each other. The forward feet are both on the same side of the dojo
(that is, left-foot-to-right-foot / right-foot-to-left-foot).
Strangely (one of those weird things), gyakute dori
is grabbing one's partner's same hand
(that is right-to-right, or left-to-left). Gyakute dori is typically done from ai hanmi. Go figure.
is (typically*) where the hands are both on the same side of the dojo
(that is, left-hand-to-right-hand/ right-hand-to-left-hand). Katate dori is typically done from gyaku hanmi.
Anyway, I just wanted to come back with what I found out.
So the terminology for hanmi vs. dori seems reversed, but at least now I know which is which. The closest I can get to making sense of that apparently inconsistancy (not saying this is the correct explanation, mind you
) is possibly what Carl Thompson said, about grabbing things the other-than-normal way (a backhand in tennis, or picking up a frying pan when the handle is facing away from you). The -dori usage could come from that "backwards grab" sense, rather than anything to do with being the "opposite" of one's partner
, where maybe the hanmi usage does mean the "opposite" stance relative to one's partner. (Partners have different feet forward, and so are in opposite stances, or are opposite in the mirror-image sense.)
Sensei mentioned the other terminology brought up here (*katate dori could mean either kind of grab, and kosa dori meaning the cross-hand kind of grab). What we use at the dojo was what he learned. No problem there. I'm glad I just finally have a grasp on it.
I wonder which kind of grasp that is, now...?