In a diminished triad, the diminished interval is 1>5. In a full diminished seventh chord, the 1>7 is also diminished. In a half-diminished chord, the 1>5 is diminished.(But one third of it still has a minor third!).
The third is always m3, and that sounds good. But what is the technicality behind 'it must be m3'. Theoretically, one may expect dim.3, but that's not good. I realise it sounds better with m3, but that's m3.