No, when you purchase online you are identified by clicking through say the American website, they use an affiliate link.

When shopping retail, you have to register your credit card first. When you swipe that card, the company running the program compares your card number to the list of registered cards, if you are one of them it processes the credit of miles to your account, if you are not it just processed the charge like normal.

In the first method, buying online, you can use any card and get the points or miles, you do not need to register it first, but you must go through the "shopping mall" except for some stores that actually ask you if you want it credited to a mileage program (most don't).

In the second method, all you need to do is use a registered card at the merchant to get the credit, same as the dining program.