Hi,
The easy part first... Sayu Gyaku means "both sides"; literally, "left" (sa), "right" (yu), "reverse" (gyaku). As for kata or henka, I was first taught them (and continue to teach them) as kata, but I have also seen them presented as henka to the main kata (Kocho Gaeshi, Tsuki no Wa, Kiri Age, Kiri Sage, etc). If I remember correctly, Hatsumi Sensei's book on Kenjutsu (Japanese Sowrd Fighting - Secrets of the Samurai) gives on average three "sayu gyaku" henka to each primary technique. I would suggest that would be a good place to start to make up your own mind, coupled with the Ken, Tachi, Katana DVD, which covers the majority of the Kukishin Biken syllabus.