X-ko
Ko is an ambiguous term. It refers to one particular shape, a class of shapes, a particular nature of a fight, the fact that a ko shape is under fight, etc. The most frequent usage is for the 2 adjacent intersections and its basic ko shape. To reduce ambiguity, the nature of a ko should not also be called "ko". Therefore, a new term shall be introduced:
An x-ko is a ko with x approach-moves that one side has to make while for the other side the ko is direct.
So a 0-ko is what was called a direct ko. A 1-ko is an indirect ko with 1 approach move (also called 1-move approach ko or 1-move approach move ko). A 2-ko is an indirect ko with 2 approach moves (also called 2-move approach ko or 2-move approach move ko). Etc.