There are 12 notes in an octave, separated by half-tones. Say you choose 7 of these notes to be in your scale. Then there are 792 possible scales. But a lot of them are pretty goofy.
So suppose the space between consecutive notes in your scale is never bigger than a whole tone. Then there are only 21 allowed scales!
These scales must have 2 consecutive notes a half-tone apart, and 5 a whole-tone apart. For example the major scale has spaces like this:
w w h w w w h
This is why there's a group of 2 black keys on the piano and then a group of 3. By cycling this pattern around we get a total of 7 scales, called the modes of the major scale.
But the melodic minor scale is not among these, because it has spaces like this:
w h w w w w h
If we designed the piano with this scale in mind, it would have a group of 1 black key and then a group of 4. By cycling this pattern around we get 7 more scales, called the modes of the melodic minor scale.
There are also 7 scales where the two half-tone steps are right next to each other, like this:
w h h w w w w
But these are more awkward, and less commonly used.
The 7 modes of the major scale have standard names, listed here. Ionian is just another name for the major scale itself.
The 7 modes of the melodic minor scale have lots of different names, and in some cases I'm not even using the most common names! For example, nobody ever talks about "Ionian ♭3" - everyone calls it melodic minor, or 'melodic minor ascending' to be precise. But I'm using names that emphasize how you can get these modes by slightly tweaking the modes of the major scale. You get melodic minor by flatting the third note in Ionian.
