What's common in the United States is a "gift registry" run by a big department store, especially one that "has nice things" but also has stores all over the United States and an online store as well. It's done electronically, and the couple enters their list, perhaps online, of things that can all be bought at the store.
When friends and family go to shop, they check the gift registry and see what things on the list have not already been bought by someone else.
This avoids annoying situations like a couple getting gifts of six expresso machines and having to return five of them.
It also helps in situations where the couple would like an expensive matched set of things, without having to put anyone in the situation of buying all or nothing. Rich Uncle Henry can buy them the twelve-setting set of plates, while their impoverished student friends can just buy them the set of bowls.
In the U.S. some people--not all--feel that it is impolite to give actual money (although my experience is that couples like to receive it!) We have a saying that "it is the thought that counts" and an ideal of buying a personalized, thoughtful gift, large or small. Also, people kind of like seeing a nice heap of gifts on a table at a wedding, even though everyone knows that the little envelopes on the table--which have checks or money in them--may be worth more than the boxes of down quilts and wineglasses and slow-cookers.
That's my best explanation of the custom.
Gift registries began years ago, and could just be a printed list kept at a big department store, but have become more popular now that they are electronic.