A church yard sale, AKA a rummage sale, is a very special type of yard sale in which the people doing the selling do not have an emotional attachment to what they are selling, have way too much stuff, and just want it gone.
Church yard sales tend to be much bigger than other yard sales, because they have many more people donating their junk. Church yard sales tend to view all this junk as fairly uniform, and price things by category (e.g., all books, 50 cents). And towards the end of the day, when some poor organizer is standing there looking at all the mountains of leftovers they are going to have to lug over to Goodwill, you can often get a lot of stuff heavily discounted.
But wait, there's more! The church wants to make some money -- this is a fundraiser first, and a way to dispose of junk second -- so they will often lump in other money-making projects. Food is sold, from fresh-grilled 'plates' of barbecue, fish, or chicken to homemade treats to cheap snacks not meant, but absolutely sold, for individual resale. Young kids sell arts and crafts. Cars are washed. There may be a silent auction, a service auction, or a raffle. Some churches include a plant sale, bake sale, branded t-shirts, or just cheap coffee.
That said, this is not usually anything like the traditional British village fete; there are rarely fun and games, and despite the long list above, most churches will only include one or two of the possibilities, and few will manage more than four different events.
As is traditional in America, yard sales, even big fancy yard sales, tend to run from about 7am to noon, and if you show up late, you're out of luck.