The pic that you mention in your second post is of Michael Douglas, as Gordon Gekko in the original "Wall Street" film.
I've seen plenty of business shirts with a contrasting white collar, and sometimes white cuffs, too, similar to the one that Michael Douglas is wearing.
However, I don't think that I've ever seen a shirt with a button-down collar in white, in contrast to the rest of the shirt. Sorry, I haven't watched the clip, so I'm not quite sure what you mean, but this is what is usually meant by a button-down collar (as you can see that the collar ends button down onto the body of the shirt:
Or do you just mean a shirt that buttons up (ie a business shirt, like the one that Michael Douglas is wearing in your pic) instead of a more casual polo shirt?
If you want a shirt like the one that Douglas is wearing in your pic, take a look at RL Polo or at a wide variety of other shirt stores, as whilst they're not really common, the style is not that uncommon, either, and you should be able to find one somewhere without too much difficulty.