Skaven clans question

I don't quite understand how building an army works in terms of lore. For example, is every clan Skryre unit actually from clan Skryre, and should be painted in their colour scheme? Or do other clans have their own clan Skryre type units painted in their own clan colours?

I know the obvious answer is to paint them however I like, but just in terms of the lore, if you see an Arch-Warlock for example, will they always be from clan Skryre?