A two-mode ring gain-noise laser model taking account of full saturation effects with multiplicative noise induced by gain fluctuations is concerned. An exact analytical expression for laser intensity distribution is obtained on resonance with equal mode pump parameters. It is found, through a comparison with the currently used models where multiplicative noise arises from loss fluctuations, that the occurrence of nonlinear multiplicative noise coefficient weakens the anomalous characteristics brought about to the laser intensity statistical properties by introducing multiplicative noise, and this kind of weakening is more apparent for larger multiplicative noise or smaller laser loss.