Hi Rinshin,
At least with American cookbooks, I figure the author means the lighter colored version when they list light soy sauce. On the other hand, I don't know that I would own a cookbook that wanted me to use lower sodium soy sauce, which I don't like the taste of.
I don't think I have seen low sodium specified anywhere other than diet books. I usually opt to use a little less than is called for and adjust to taste.
Zephy