There is indeed a description, however it is yet unfinished and it was made for the Katarai - it needs to be adapted to the others. Anyway, the physical description will probably not become public, I think it is best that the physical traits of the elves are transmitted visually (i.e. concept art).
They all look identical, because they are all the same elves. They are not only one race, but also one country - each of the sects is under the same rules and has the same basic culture. In fact, they only split about 1500 years ago or so - there was no time for a new race to develop.
Like you say, they are distinguished through their clothing, attitude and some of their culture. Not through language nor gait. There are some physical differences, but nothing too prevalent. For instance, blond hair is more common among the Katarai than the Iliai, but there are some blond Iliai, the same way that blond hair is more common in humans from a certain origin than those from another. Also, the Iliai and the Katarai have darker complexion, but that's because they live in sunny areas and wear little protective clothing.
An elf would recognize whether the other was Katarai, Iliai or Veliai, independent of clothing, but outsiders would not.
In my mind the player will start as an elf, being able to chose any physical aspect he or she wishes, and then it will be through gameplay that eventually (s)he will become (or not) a Katarai, an Iliai or a Veliai.