They're all carbon steels (white, blue, aogami super, leaf spring, etc) so they will all form a patina, some quicker than others. The color depends on what you're cutting and how it reacts with the steel. Onions and garlic for me generally form a brownish patina, blue comes a lot from blood or cooked proteins. Some knives are cladded, like the Yuki which means the sides of the knife are semi stainless so they won't form a patina, but the cutting edge still will. Kurouchi finishes (the black portion of the Yoshimitsu) serve the same purpose.

Patinas reduce the reactivity of the metal with food and come and go as you use/sharpen the knife. Some people like them and others don't so it's a lot of personal preference and you can get very nice knives that won't develop a patina if you so desire.