It's true that voiced aspiration is just breathy voice. But breathy voice is a related phenomenon to aspiration, and it therefore makes sense for voiced aspirated stops to be referred to as such.
To aspirate a voiceless stop which is immediately before a vowel, you keep the voicelessness going for longer than usual (before initiating the voicing which accompanies the vowel). That means you have to close the glottis more slowly. A natural way to do that is to have the vocal folds further apart than normal when the stop is articulated, so that, even if the glottis is closed at the same speed as normal, the VOT will be higher. So we can also define an aspirated sound as one articulated with greater glottal spread than normal. This theory of aspiration is attributed to
Kim (1970) (I don't have access to that paper, but it's cited as such by other papers such as
Iverson & Salmons 1995 and
Jacques 2011.) It's the reason the contrast between aspirated and unaspirated voiceless stops is normally represented in terms of distinctive features by the contrast between [+spread glottis] and [-spread glottis].
One of the advantages of this definition is that it also works for aspirated stops in word-final position and before voiceless segments. And it can also be applied to voiced segments. A voiced segment is aspirated if it's articulated with greater glottal spread than normal, and if a segment is articulated with greater glottal spread than normal, but it's still voiced (the vocal folds are close enough that they vibrate), then that's what we call breathy voice. (Breathy voice in Hindi, and presumably other Indo-Aryan languages, is actually not exactly like this: what happens is basically that part of the glottis is closed as if to produce modal voice, but another part of the glottis is open as if to produce voicelessness. But it has a similar acoustic effect, and it's still reasonably to describe it as a [+spread glottis] articulation, it's just that only part of the glottis is spread, and it's spread completely, rather than the whole of the glottis being spread partially.)
As evidence that Indo-Aryan voiced aspirates phonologically pattern with voiceless aspirates, you could probably cite some Grassman's Law examples where a voiced aspirate was deaspirated before a voiceless aspirate or vice versa. I don't know any such examples offhand though.
There is at least one language (Kelabit, see
Blust 2006) which has "true" voiced aspirates: these are just voiced stops for which, after or just before the release, the glottis is abruptly opened for a short while, but then closed again in order to voice the following vowel. Essentially, then, they're just voiced stop + [h] clusters which are phonologically unitary phonemes. In Kelabit they are always geminate and intervocalic, and the voicelessness usually begins some time before the release so you have [bpʰ], [tdʰ], etc. But these are very unusual segments.
