[GRASS-user] Stream distance - Elevation

Dear GRASS GIS community,

trying to compute the HAND model:

Nobre A. D., 2001 http://dx.doi.org/10.1016/j.jhydrol.2011.03.051

i'd like to get pixels from 0 to 2 meters higher than the stream pixel
they flow in (hoping i haven't missed any point in these papers).

I used
r.stream.distance difference=elevation_from_stream
with
r.mapcalc 'hand = elevation_from_stream < 2'

Comparing to a previous output computed using ArcGIS, differences appear.

Is it assumed that elevation difference is computed from the stream
pixel a pixel flows in (i.e following flow direction map)?
Or, is it in relation to the closest stream pixel ("as the crow flies"
distance)?

Would there be a difference providing the r.fill.dir output flow
direction map instead of the r.watershed one?

Many thanks in advance,

regards,

Adrien