jimvance

Kote means forearm and kaeshi means roughly "to return". Wrist twisting would be "tekubi hineri".
With that said, Japanese nomenclature has undergone a lot of changes. In the feudal era, techniques were not done as single faceted movements; they were incorporated into larger kata that developed timing, strategy, posture. Since it was a feudal time, teachers did not always want other schools learning what they were teaching. This disguising of nomenclature is apparent in the weaponmaking vs. armormaking arts of feudal Japan. Take also into account that during the Tokugawa regime, people were not allowed to leave their areas (villages) without permission from a governmental authority. Different names of techniques, even though technically similar, abound.
Within the "Daito Ryu" (which was not called that until two "generations" before Ueshiba received its teachings) we have things like the ikkajo (ikkyo), the nikkajo (nikkyo), etc. These are not descriptive at all, reflecting the feudal mindset towards education and suspicion of other schools.
Then a man named Jigoro Kano comes along and starts Judo and offers a new public martial art devoid of old license requirements, replacing it with a belt ranking system. He takes the names of techniques from two older jujutsu schools and names them according to principles and descriptions the average Japanese person can understand. Voila, new nomenclature, that would later be absorbed by other new budo like kendo and aikido in method. The "middle children" of Ueshiba Sensei had a lot to do with naming the techniques we know of today, and there was a lot of cross pollination between gendai budo schools during the time. Unfortunately, the result of that in the West is that we are results oriented rather than process oriented, and so we view the techniques as independent outcomes, rather than through the classical model of skill sets developing strategy, timing, etc. The terminology reflects this mentality. New teachers have come along and recognized this deviation, and there is now a return to the classical from the perspective of the modern. So that leaves us the job of determining what is significant (and giving new meaning to the usage of terms, if necessary, like Colleen says) and keeping things pure (like kote gaeshi).

Jim Vance