Chromatic transposition, which moves each note by the same number of semitones (e.g. C E G to D F# A) is clearly useful to change the key of a song. I just heard of diatonic transposition, which moves each note by the same number of steps in the scale (e.g. C E G to D F A in C major). However, this must change up a melody or chord progression completely, right?
When is it useful to think in terms of diatonic transposition? I realise that this operation preserves the key, but what does it do and why is it useful? Can it still be considered the same melody or chord progression?