The spectral behavior of the intensity noise correlations between the two orthogonally polarized modes of a dual-frequency Nd:YAG laser is investigated, both experimentally and theoretically. We show, for different coupling strengths between the two orthogonally polarized modes, how the presence of the relaxation oscillations due to the class B dynamical behavior of our laser affects the shape of the intensity noise correlation spectra. Different coupling situations have been achieved by controlled alignment of the two orthogonally polarized oscillating modes with respect to the crystallographic axes of a ⟨100⟩-cut neodymium-doped yttrium aluminum garnet active medium in which the light-emitting dipoles behave as if they are aligned along the crystallographic axes. The theoretical modeling has been done based on the assumptions that the only source of noise for the two lasing modes in the interesting frequency range (0-120 kHz) is the intensity noise of the pump diode laser, the pump noises for the two modes are white frequency noises of identical amplitudes, and the pump fluctuations are in phase, but partially correlated.