  The discrepancy between a LONG distance scale derived from Hipparcos based
distances to globular clusters via main sequence fitting to local subdwarfs,
and a SHORT distance scale derived from the absolute magnitude of field RR
Lyraes via statistical parallaxes and the Baade-Wesselink method could be
accounted for whether an intrinsic difference of about 0.1-0.2 mag was found to
exist between horizontal branch (HB) stars populating the "sparse" general
field and the "dense" globular clusters. In this paper we discuss the possible
existence of such a systematic difference comparing the "period-shifts"
observed for field and cluster RR Lyraes. Various approaches based on different
parameters and data-sets for both cluster and field variables were used in
order to establish the size of such a hypothetical difference, if any. We find
that on the whole very small not significant differences exist between the
period-metallicity distributions of field and cluster RR Lyraes, thus
confirming with a more quantitative approach, the qualitative conclusions by
Catelan (1998). This observational evidence translates into a very small
difference between the horizontal branch luminosity of field and cluster stars,
unless RR Lyraes in Globular Clusters are about 0.06 Mo more massive than field
RR Lyrae at same metallicity, which is to be proven.
