I have very light blonde hair and I have found that shampoo/conditioners for dry/damaged hair work better for me than ones for coloured hair. But don't they always say if you have coloured hair use a shampoo/conditioner for coloured hair? Which are the best?
coloured hair is damaged hair - by adding colour to your hair you are damaging the hair. But shampoos for coloured hair help to make the colour last longer
Shampoo for dyed hair is generally supposed to be milder, less alkaline I think, probably very similar to formulations for dry hair. Shampoo for dyed hair also may have UV protection in it, which shampoo for dry hair wouldn't necessarily have.