Hi, Gunplummer, if you find out, let me know. I have been digging around for a long time and can't find the answer. I am not even sure the Japanese didn't call it that.
Hi, 44AMP, I think the confusion was probably more for modern collectors than for the Japanese. The 7.7 rimless was issued only in clips that fit the Type 99 rifle. The 7.7 semi-rimmed was issued only in feed strips for the Type 92 HMG, and the 7.7 rimmed (.303 British) was issued only to the Navy for their Lewis guns. So there would be few if any chances for confusion.
I think there would have been greater chance for a mixup with the two types of rifle ammo, but they reportedly made sure a given regiment or division had only one caliber rifle.