Northeastern U.S. here. Flea markets (the closest equivalent of car boot sales in the U.K.) have changed a lot since I was a youngster in the 1960s/early '70s. My parents used to exhibit at a large flea market in southern New Hampshire that was mostly antiques dealers selling glass and china, old tools, antique toys and such. There were also food booths and some specialty vendors -- one I remember was a fellow who would draw portraits on site. I never saw folks selling the sort of plain old secondhand stuff (used clothes, toys, etc.) that you'd see at a garage/yard/tag sale.
The flea markets I attended in the '80s were mostly populated by vendors selling new but cheap goods -- hats, key rings, T-shirts, costume jewelry, etc.
Around here these days, we have a lot of village-wide and town-wide garage sales, where people sell their own stuff from their own garages/yards and keep the proceeds. You can register your sale with the organizers (sometimes for a fee, sometimes not), and it gets put on the map they give out to visitors. Or you can just set up your own sale on town-wide sale weekend and let people find it as they drive around.
Or you can simply have your own sale on whatever day you choose. Hard-core "garage salers" check the classified ads and drive around to the sales they see advertised.
Churches and other organizations have rummage sales for which they solicit donations of goods to sell. The money goes to the church/organization. I used to volunteer with an organization that did a sale like this, and it was a nightmare! We solicited donations from the community, and everyone brought over the stuff they didn't sell at their *own* garage sales. (Translation: lots of junk nobody wants.) Fortunately, there was a charity thrift shop that offered to cart our unsold merchandise away. Otherwise, we would have had to pay more to get rid of it than we made on the sale.