My definition of a full caster would actually be based on his utility to his party.
Allow me to offer way number 4:
4. A "full caster" is a character that can provide a wide variety of magic spells no matter the situation. That is, just because he's known for knowing Forcecage doesn't mean he can't also cast Etherealness, Magnificent Mansion, Plane Shift, Simulacrum, or Teleport. All of these are spells that are "good to have", but perhaps not *critical*, so a less flexible, a less "full" caster, can't afford to choose either of them. A "full caster" can assume the responsibilities as a party's sole caster, so let's not forget about area damage spells. He also can nova in critical situations, expending a significant number of powerful spells for many combat rounds in a row.
Obviously, this definition overlaps with both #2 and #3. But I would like to argue that these definitions are more of technical details that doesn't necessarily have to be true (perhaps the Psion/Mystic will manifest some of this).
Perhaps a nitpick, perhaps not.