Aha! I understand it now. Or at least I think I do.

diminished chord is 1 3b 5b (Cdim)
diminished seventh is 1 3b 5b 7bb (Cdim7)
half-diminished is 1 3b 5b 7b (minor seventh) (Cm7b5)

just to confuse things:

"In most sheet music books, Cdim or C° denotes a diminished seventh chord (a four note chord) with root C, and Cm-5 or Cmb5 denotes a diminished triad with root C. Howevever, in some modern jazz books and some music theory literature, Cdim or C° denotes a diminished triad, while Cdim7 or C°7 denotes a diminished seventh chord." (wikipedia)

and

"Half-diminished seventh chords are often symbolized as a circle with a diagonal line through it, as in Cø.

The terms and symbols for this chord break the usual system of chord nomenclature. Normally a symbol like "Bdim" indicates a diminished triad and "B7" indicates a major triad plus a minor seventh. Thus one would expect the term "Bdim7" to indicate a diminished triad plus a minor seventh. Instead, it means a diminished triad plus a diminished seventh. To make this distinction clear, the term "half-diminished" and the ø symbol were invented. Since the term dim7 (as in Bdim7) meant something else, the accurate but unwieldy term "minor seventh flat five" (as in Bm7(b5)) came to be used." (wikipedia)

So if I were to enter Cmb5 in Biab - would it still give me the seventh, I wonder?

Learning a lot here! Mel