I can’t tell the difference between › ‹ and ↷ ↶ under the circle. They both sound like they change the notes.
These are separate operations.
› ‹ moves the mode to the next one. The tonic stays the same, and only the order of notes changes. In C major, pressing › gives you C Dorian, with E♭ and B♭ appearing. Keep pressing and you’ll cycle through all seven modes starting from the same C.
↷ ↶ is transposition. The entire scale, including the tonic, moves by a semitone. The star shape stays the same; it just rotates — C major → C♯ major.
⇅ is inversion, and it leaves you with a scale made only of notes that aren’t sounding. The inversion of C major is five black keys, which is the pentatonic scale.
The easiest way to hear the difference is by ear: click › seven times in a row — the tonic doesn’t move, but the mood changes every time.