  In this letter we present a morphological comparison between giant radio
halos and radio mini-halos in galaxy clusters based on radio--X-ray luminosity,
P_{1.4}-L_X, and radio luminosity-size, P_{1.4}-R_H, correlations. We report
evidence that P_{1.4}-L_X and P_{1.4}-R_H trends may also exist for
mini--halos: mini--halo clusters share the same region of giant halo clusters
in the (P_{1.4},L_X) plane, whereas they are clearly separated in the
(P_{1.4},R_H) plane. The synchrotron emissivity of mini-halos is found to be
more than 50 times larger than that of giant halos, implying a very efficient
process for their origins. By assuming a scenario of sporadical turbulent
particle re-acceleration for both giant and mini halos, we discuss basic
physical differences between these sources. Regardless of the origin of the
turbulence, a more efficient source of injection of particles, which eventually
takes part in the re-acceleration process, is required in mini-halos, and this
may result from the central radio galaxy or from proton-proton collisions in
the dense cool core regions.
