Question: In a song I am learning, there is a section of the song that has the chord progression G#m | A#m7b5 | B6
I sometimes get the fingerings wrong and use dimished 7th chords on guitar instead of m7b5 chords and in this case I actually think the dimished7th chord sounds good too. So I wanted to ask, what is the difference functionally between the two? They both seem to work in most situations as leading tone chords to a tonic chord one semitone above (B in this case).

Answer: 
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> Do m7b5 chords function the same as dim7 chords?
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If talking about function, it seems better to not use jazz chord symbols and switch to using Roman numeral analysis (RNA.)

The two chord types are *half-diminished seventh* and *diminished seventh*.

The diminished seventh chord is easier to describe first. Usually it is rooted on the *leading tone* or a *secondary* leading tone. Its RNA symbols is `viio7`. Relative to a tonic of `C` the chord would be spelled `B♮ D F A♭` (I used the natural to show that in `C` minor you would raise the `B♭` of the key signature.) The chord's basic *function* is a dominant and in that regard some people conceive of the chord as a dominant flat ninth chord with the root omitted.

The half diminished seventh chord is a bit more complicated. In major keys it is the *diatonic* seventh chord built on the leading tone. In `C` major it would be `B♮ D F A♮` and the RNA symbol would be `viiø7`. If that chord were used in a major key, its function would be a dominant. But, the chord is actually much more common in minor keys where it is the *diatonic* chord build on the second scale degree. In `C` minor is would be `D F A♭ C` and its RNA would be `iiø7`. The function of `iiø7` is a *subdominant*.

The typical function of these chords is *not* the same. `viio7` is a dominant. `iiø7` is a subdominant.

Those roles also apply to basic jazz harmony.

The diminished seventh chord can appear as a dominant or as a passing chord. The song *Bewitched* uses the chord both ways. It starts with `C C♯dim7 Dm7` or in RNA `C: I viio7/ii ii7`.

The half diminished seventh chord appears in minor, like `iim7♭5 V7alt im6`. *Autumn Leaves* is an example.
The basic triad (which is what usually gives the main "color" to the chord) is the same, and being a diminshed fifth it creates a lots of tension towards the next one - usually a half tone above, and usually the tonic.

They *are* similar and often interchangeable. While they are not diatonic on both major and minor mode, they can "exist" in those modes:

* in minor mode, the root and seventh of m7b5 are the seventh and sixth melodic degrees ("augmented");
* in major mode, the seventh of dim7 is the harmonic ("lowered") sixth;

The lowered sixth "sounds good" in both modes because it creates a big tension that leads to the fifth, and also due to the fact that it creates another tritone with the third of the chord.

The m7b5 chord is usually considered less powerful than the dim7, as the seventh has less tension towards any resolution, but it can still create interesting effects. The choice depends on the composer/arranger/performer, but it obviously should not collide with any other voice (the melody) and should consider the overall harmony and current harmonic progression.