One of the classical experiments of psychoacoustics is the measurement of the lowest sound level at which a tone is heard in the presence of a white noise masker. This sound level is called the 'masked threshold'. In the following example, the masker is played at a fixed level, and the level of the tone can be adjusted. On every repeat of the stimulus, the masker is started first, and a short time later the tone comes in.
Set the tone to a level at which you can hear it clearly. Introspectively, the sounds differently - it is as if two 'objects' were playing at the same time.
Next, find your masked threshold. What happens for tone levels that are very close to masked threshold? Do you still hear the tone as a 'different thing'?