Context :

Aims : This work uses nonlinear convective models of RR Lyrae stars and evolutionary predictions of low-mass helium burning stellar structures to constrain the properties of cluster and field RR Lyrae variables .
In particular , we address two problems : is the Period-Amplitude ( PA _ { V } ) plane of fundamental ( RR _ { ab } ) variables a good diagnostic for the metal abundance ?
Is the M _ { V } ( RR ) - [ Fe/H ] relation of field and cluster variables linear over the whole metal abundance range of [ Fe/H ] \sim - 2.5 to \sim 0 ?

Methods : We perform a detailed comparison between theory and observations for fundamental RR Lyrae variables in the solar neighborhood and in both Oosterhoff type I ( OoI ) and type II ( OoII ) Galactic globular clusters .

Results : We show that the distribution of cluster RR _ { ab } variables in the PA _ { V } plane depends not only on the metal abundance , but also on the cluster Horizontal Branch ( HB ) morphology .
We find that on average the observed pulsation parameter k _ { puls } , connecting the period to the visual amplitude , increases when moving from metal-poor to metal-rich GGCs .
However , this parameter shows marginal changes among OoI clusters with intermediate to red HB types and iron abundances -1.8 \leq [ Fe/H ] \leq - 1.1 , whereas its value decreases in OoII clusters with the bluer HB morphology , although these clusters are also the less metal-poor ones of the group .
Moreover , at [ Fe/H ] = -1.7 \pm 0.1 the OoI clusters present redder HB types and larger \langle k _ { puls } \rangle values than the OoII clusters .
The RR _ { ab } variables in \omega Cen and in the solar neighborhood further support the evidence that the spread in [ Fe/H ] , at fixed k _ { puls } , is of the order of \pm 0.5 dex .
Using the results of synthetic HB simulations , we show that the PA _ { V } plane can provide accurate cluster distance estimates .
We find that the RR _ { ab } variables in OoI and in OoII clusters with very blue HB types obey a well-defined M _ { V } ( RR ) - k _ { puls } relation , while those in OoII clusters with moderately blue HB types present a zero-point that is \sim 0.05 mag brighter .
Regarding field variables , we show that with [ Fe/H ] \geq - 1.0 a unique M _ { V } ( RR ) - k _ { puls } relation can be adopted , independently of the color distribution of the parent HB star population .

Conclusions : Current findings suggest that the PA _ { V } distribution does not seem to be a robust diagnostic for the metal abundance of RR _ { ab } variables .
However , the same observables can be used to estimate the absolute magnitude of globular cluster and field RR _ { ab } variables .
Eventually , we show that over the metallicity range -2.4 \leq [ Fe / H ] \leq 0.0 the M _ { V } ( RR ) - [ Fe/H ] relation is not linear but has a parabolic behavior .