Level Up is a support ability, mostly found on pieces of equipment, namely accessories, that usually doubles the amount of EXP that a character earns from battles. It is an ability that is usually gotten around midway to late in the game.
Level Lust is an ability gained from an augment found in the Hummingway Home in the DS version of the game. It is a support ability that increases the amount of EXP gained from battles. It can be obtained multiple times via the New Game Plus feature.
Level Up is an ability found in EXP. Egg, which can be equipped by everyone. It is found in Darill's Tomb, in a hidden room after completing a puzzle. It can also be obtained from the Colosseum by betting a Tintabar, or morphed from Harpy, Harpiai, and Aquila.
Level Up is an ability found on the EXP Plus materia. At Level 1, it increases EXP earned by x1.5, and at Level 2, by double. The EXP Plus materia can only be obtained after Meteorfall at the Gold Saucer, in the Wonder Square, for 1000 GP.
Level Up is an actual ability that must be learned, and can be learned by everyone. It is learned through Iron Helm, Egoist's Armlet, Extension, Fairy Earrings, Pearl Rouge, and Rosetta Ring.