That is exactly what happens in India too, except that most banks issue debit and credit cards which are typically separate and not combined into a single card. It also does not serve as a national id. Is this not the case in US?
Basically the same here. I have both debit and credit cards are from the same bank. National id is a bit more contentious here but generally the two cards are about the same. With the caveat of much lower daily withdrawal limits on the debit (think 300).