The diminished seven (1-b3-b5-bb7) and half diminished seven (1-b3-b5-b7) chords are built upon a diminished triad. Despite this similarity and despite the tendency of some musicians to treat these chords the same, the two can function very differently. Each can serve in a dominant function and resolve to a major or minor triad whose root is a half-step higher. However, the half diminished seven also functions as a subdominant chord in minor keys (iiø7 – V7 – i7). The ii-V relationship is one of the most common harmonic idioms in jazz and popular music. The fully diminished seven chord almost always functions in a dominant capacity. It is one of the most easily transposable chords in music and serves as a handy device for transposing to far-off keys. All this put aside, let it be said that these two chords offer very different possibilities for use in music.
The Diminished Seven Chord

C diminished 7 (C – Eb – Gb – Bbb)
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The Half Diminished Seven Chord

C Half Diminshed 7 or Cm7b5 (C – Eb – Gb – Bb)
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