  We present the first systematic study of X-ray flare candidates in short
gamma-ray bursts (SGRBs) exploiting the large 6-year Swift database with the
aim to constrain the physical nature of such fluctuations. We find that flare
candidates appear in different types of SGRB host galaxy environments and show
no clear correlation with the X-ray afterglow lifetime; flare candidates are
detected both in SGRBs with a bright extended emission in the soft gamma-rays
and in SGRBs which do not show such component. We furthermore show that SGRB
X-ray flare candidates only partially share the set of observational properties
of long GRB (LGRB) flares. In particular,the main parameter driving the
duration evolution of X-ray variability episodes in both classes is found to be
the elapsed time from the explosion, with very limited dependence on the
different progenitors, environments, central engine life-times, prompt
variability time-scales and energy budgets. On the contrary, SGRB flare
candidates significantly differ from LGRB flares in terms of peak luminosity,
isotropic energy, flare-to-prompt luminosity ratio and relative variability
flux. However, these differences disappear when the central engine time-scales
and energy budget are accounted for, suggesting that (i) flare candidates and
prompt pulses in SGRBs likely have a common origin; (ii) similar dissipation
and/or emission mechanisms are responsible for the prompt and flare emission in
long and short GRBs, with SGRBs being less energetic albeit faster evolving
versions of the long class. Finally, we show that in strict analogy to the SGRB
prompt emission, flares candidates fall off the lag-luminosity relation defined
by LGRBs, thus strengthening the SGRB flare-prompt pulse connection.
