In L5R, like so many other mechanics, Wound Rank does indeed refer to the various categories of wound, such as Healthy, Nicked etc. The individual points of damage are usually referred to as Wound Points.

This mirrors the mechanics used for Glory Points/Ranks and Honor Points/Ranks, and even Shadowlands Points/Ranks. A number of Wound or Damage points equal to or greater than a Wound Rank means you suffer the effects of that Rank.

About the Permanent Injury, yes, it fills up the Healthy Wound Rank. A character is considered to be at whatever Wound Rank is not completely filled, so normally, up until Wound Points equal to the Healthy Rank, he would be Healthy. This character is never Healthy.

(Additional info) There is a definition for wounds on p82 of the 4e rulebook, and p166 of the 3e rulebook. 

3e actually talks about Wound levels rather than Wound Ranks, but then, so does Permanent Wound (p117). 4e distinguishes between points of damage and Wound Ranks, and Permanent Wound fills in your first Wound Rank (p161). Earlier editions may have used less exact terminology.