However, the person who wrote the Wikipedia article seems to make a fine distinction: "A White Elephant Sale is a collection of used items being sold by commonly but not always a non-professional group of individuals or a group or team of individuals, much akin to a yard sale or garage sale, but more often than not usually as a fund-raiser for a various cause." https://en.wikipedia.org/wiki/White_Elephant_Sale
The difference seems to be a matter of connotation rather than strict definition. A white elephant sale just seems more interesting, and we'd expect to find fascinating items there that might not be useful but might make good conversational ice breakers - that lamp with ladies' legs in fishnet stockings or that moose head that would go so nicely over the fireplace. Of course, it fits the definition even better if it's something whose upkeep is so expensive you might need to have your own sale - like that cute whaling ship that requires you to buy a fishing village to have a place to keep it.