Up to this point, LG has only offered one form of a flexible display in a smartphone. The G Flex and G Flex 2 are curved vertically. Samsung, on the other hand, has offered a horizontal curved display in the Galaxy Round as well as the Galaxy Note Edge, which features a curved edge display.
Perhaps taking a bit of the spotlight from the new Galaxy Note 4, the Galaxy Note Edge is essentially a Galaxy Note 4 with a special curved display on the edge of the phone. Thus, the super clever name. The Galaxy Note Edge has almost identical specs to the Galaxy Note 4, save for a slightly smaller battery and, of course, a random display hanging off of the side of it.