A Pentatonic tune is just 5 tones, so using just the black keys on the piano is one way to explore them.

What a pentatonic scale lacks is semitones. In that all white key example, you'd never use both of the white keys that are adjacent in the same tune.

The Ionian/Aeloian/Dorian/Mixolydian, etc. distinctions become pretty meaningless. Omit a 7th entirely from an otherwise major tune & you can't call it Ionian or Mixolydian.

Thus Pi 1= Ionian, without the 4th and 7th (and sounds Scottish or Appalachian, or Chinese
Pi 2    = Mixolydian, without the 7th and 3d (and sounds Irish) and so on around.

You can with equal precision say:
Pi 1= Mixolydian, without the 4th and 7th
Pi 2= Ionian, without the 7th and 3d