The phenomenon of tinnitus masking (TM) and residual inhibition (RI) of tinnitus are two ways to investigate how external sounds interact with tinnitus: TM provides insight on the fusion between external sound activity and tinnitus related activity while RI provides insight on how the external sound might suppress the tinnitus related activity for a period of time. Differences in masking level between the tinnitus and an external tone with tinnitus characteristics (frequency, loudness) have previously shown a high level of heterogeneity. The difference in poststimulus suppression between the two, that is, residual inhibition for the former, and forward masking for the latter, has never been explored. This study aims to investigate minimum masking levels (MMLs) and minimum residual inhibition levels (MRILs) of tinnitus and of an external tone mimicking tinnitus while using diotic and dichotic noises. Pulsed narrowband noises (1 octave width and centered at 1 kHz, frequency of the hearing loss slope, tinnitus frequency) and white noise were randomly presented to 20 tinnitus participants and 20 controls with an external tone mimicking tinnitus (4 kHz, intensity level corresponding to tinnitus loudness). The MML values obtained for the masking of tinnitus and for the mimicking external sounds were very similar. On the other hand, the MRILs were significantly different between the tinnitus and the mimicking external sounds within tinnitus participants. They were also different between the tinnitus participants and the controls. Overall, for both within and between comparisons, the MRIL values were much higher to produce a poststimulus suppression for the mimicking sound than for the tinnitus. The results showed no significant differences between the diotic and dichotic conditions. These results corroborate other findings suggesting that the tinnitus-related neural activity is very different from the stimulus-related neural activity. The consequences of this last finding are discussed.