The spin noise mechanisms in a spin-1 system are theoretically and experimentally investigated in details. Eight different independent spin degrees of freedom are isolated, leading to spin noise signals at the Larmor frequency or its second harmonic in the presence of a magnetic field. The signature of these different modes of the detuned probe light beam polarization fluctuations, observed either as Faraday rotation noise or as ellipticity noise, are shown to depend dramatically on the probed transition. In particular, depending on the Zeeman structure of the upper level of the transitions, the different noise modes can be visible or not, and their dependence on the probe polarization can be completely modified. Those predictions are successfully compared with measurements of spin noise signals using three different transitions of an ensemble of metastable 4 He at room temperature.