Any particular use for the first one ?. And why they're using "me le te" instead of "ri si li" while ascending ?. Is it because C minor is E flat Major ?.
There are actually three minor scales: natural, harmonic, melodic (but, for melodic, ascending and descending are different).
In the key of A minor (no sharps or flats), we have:
Scale type
Ascending
Descending
Natural minor
A
B
C
D
E
F
G
A
A
G
F
E
D
C
B
A
Harmonic minor
A
B
C
D
E
F
G#
A
A
G#
F
E
D
C
B
A
Melodic minor
A
B
C
D
E
F#
G#
A
A
G
F
E
D
C
B
A
The raised 7th degree (G#) in the harmonic and ascending melodic minor scales arise principally because the of 7th degree being the "leading tone" to the 8th degree (A). The raising of the 6th degree (F#) in the ascending minor scale comes about from a principle or tradition that "normal" (?) scales should have steps that are either whole steps or half-steps. In the descending scales there is no "requirement" or "necessity" for the 7th degree to be raised a half step (since it is not leading to the 8th degree), so the descending melodic minor and natural minor scales agree.
Chuck
Charles H. Giffen CPDL Board of Directors Chair
Admin at & Manager of ChoralWiki
Regarding the solfeggio questions (as opposed to minor scales in general, which Chuck has explained very nicely), me, le, and te are used instead of ri, si, and li because of the notes function in the scale. That is, the me takes the place of the mi in the major scale, being the third note in the scale and occupying the same sort of position in chords and so forth. It's also a reason why the C minor scale is written using flats (either in the key signature with accidentals) rather than sharps. I suspect that most people find it more convenient to translate between written-out music and solfeggio when the notation and the syllables correspond.
The second form you have shown, starting on la rather than do, serves mainly to emphasize the relation between the minor key and its relative major key. I personally find this approach rather more confusing and troublesome than helpful, but I'm sure there are people who find it otherwise. Likewise, I tend to think of C major and A minor as different keys when (attempting to) play the piano, despite their having the same key signature.
Starting a minor scale with "Do" rather than "La" makes the "Do" syllable always be the tonic of the key.
"Di", "Ri", etc. are not so much used solely when ascending, but rather are used when the corresponding scale degree is raised a semitone (which would of course be notated using a sharp or a natural). For a chromatic scale, these are generally used when ascending because that's the standard notational convention, doubtless to avoid using extra unnecessary accidentals. Likewise, for a descending chromatic scale, the appropriate notes are lowered a half step for similar reasons. In other contexts, though, whether use a raised or a lowered note is dictated by other things; a (minor) seventh in a chord would always use "Te" rather than "Li", for example, as it's properly notated as the seventh note lowered by a half-step rather than the sixth raised a half step.
Using the syllables do-re-me versus la-ti-do is indicative of whether one subscribes to the fixed-do or movable-do school of solfege. See http://en.wikipedia.org/wiki/Solfege, which in fact gives the natural minor scale as an example.