Hi Sorana,
The traits you see on SL are the cat's costume, the ones you see on the pedigree
are the "real" traits.
Each cat has 2 "layers" of traits, one visible (the one you can see for sure on the
pedigree page) and one hidden (that you have to figure out through breeding).
But some cats, like the Limited Editions or some "special kittens" they usually
get as their first kitten, have 3 "layers" of traits : the costume (most of the time,
that is not breedable/passable) and the 2 other layers I just talked about.
Hikari