  The gamma-ray emission from Starburst and Starforming Galaxies (SBGs and
SFGs) strongly suggest a correlation between star-forming activity and
gamma-ray luminosity. However, the very nature of cosmic-ray (CR) transport and
the degree of their confinement within SBG cores are still open questions. We
aim at probing the imprints left by CR transport on gamma-ray and neutrino
observations of point-like SFGs and SBGs, looking into quantitative ways to
discriminate among different transport models. Moreover, following the reported
scenarios, we quantitatively assess the SBGs and SFGs contribution to the
Extra-galactic Gamma-Ray Background (EGB data) and the IceCube diffuse
observations (HESE data). We analyse the 10-year Fermi-LAT spectral energy
distributions of 13 nearby galaxies with two different CR transport models,
taking into account the corresponding IR and UV observations. We generate mock
gamma-ray data to simulate the CTA performance in detecting these sources. In
the way, we propose a test to discriminate between the two CR models,
quantifying the statistical confidence at which one model can be preferred over
the other. We point out that current data already give a slight preference to
CR models which are dominated by advection in their nucleus. Moreover, we show
that CTA will allow us to firmly disfavour models dominated by diffusion over
self-induced turbulence, compared to advection-dominated models, with Bayes
factors which can be as large as $10^7$ for some of the SBGs. Finally, we
estimate the diffuse gamma-ray and neutrino fluxes of SFGs and SBGs, showing
that they can explain $25\%$ of the diffuse HESE data, while remaining
consistent with gamma-ray limits on non-blazar sources.
