The super-exclusive black card people are talking about is the American Express Centurion Card. This card is black in color, and given Amex's existing gold card, platinum card, etc., it's natural to refer to it as a "black card." But the product in question is a super-premium high-fee invitation-only service that probably lets you plead affluenza to any number of crimes.
The Visa Black Card, by contrast, is something that anyone with good credit and a willingness to pay $495 a year in fees can get. Which is to say that it's a product comparable to American Express' Platinum Card—a high-fee product that also comes with some nice benefits, like membership in the Priority Pass airport lounge program. The only problem is that the Black Card is slightly more expensive than the $450 Platinum Amex and the benefits are slightly worse. For example, the Platinum Card gets you Priority Pass and free access to Delta lounges. Platinum will also give you free membership in Global Entry and a $200 statement credit for airline purchases of your choice.
There's basically no reason for anyone to ever get this card. It's only confusion with the Centurion Card that would make anyone think it's a superior product. And that, in turn, is pretty clever marketing on Visa's part. All a bit trivial in the grand scheme of things, but a little reminder about how it's possible to make money by systematically exploting information failures.