My music appreciation professor told us that...
- a motif is usually an incomplete melodic idea around two to ten notes long and stands for a specific person, thing, or idea. (i.e., think the five descending notes in Phantom of the Opera - that's the Phantom's motif)
- a theme is usually a complete melodic idea that also stands for a specific person, thing or idea. (think the entire title song from Phantom of the Opera - it's repeated, both with and without words, many times throughout the whole musical)
- a song is by definition something which is sung. Instrumental music is called either by the name of what it actually is (a symphony, a sonata, etc.) or simply a "piece."
A little off topic I know, but interesting nonetheless. So I would say that Aeris' motif appears in World Crisis, cause if I remember correctly it's only the first ten notes or so, and not a complete melodic idea.
