I think it does vary from place to place.
In our area these days, we have gift registries. I wish we'd had them when husband & I got married; back then people asked us what we wanted and gave us things (mostly missing by a mile).
difficult child 1 & girlfriend have used an online gift registry which allows people to buy things generically (they aren't specifying a particular store, which has been the other option). Cash is also an option, but it too gets logged online because their thank-you cards are also aided this way.
My brother sent a wedding gift to difficult child 1 - bro is going to be in hospital on day of wedding, so can't make it. He also can't afford much but he used the online gift registry to put together a hamper of kitchen tools for the kids. I know what he bought and roughly how much it costs - it won't have cost as much as I know other people are giving, but I do know the kids really value what he sent. The main item was a set of measuring cups and a silicone cake pan - I know when they use these items, they will be thinking of their uncle who was in hospital.
I do know that when husband & I use various items in the house, we remember the person who gave it to us. In some cases, when cash was given and we put it towards something we wanted, we still remember the people who contributed.
A young friend of ours didn't want gifts because she and her new husband had been living together for some years, both were over 30 and didn't need household items. Instead they asked for money to put towards their honeymoon. The money given made more side trips possible and whenever they look at their wedding photos, I know they will be thinking of their guests who contributed.
Marg