I have a general tone (or set of tones I guess) which is around equal in both ears usually. But they will sometimes just change for a while, which is extremely jarring since generally I do get used to the constant sound that suddenly being consciously aware of it generally distracts from whatever else is going on. Sometimes that change only happens in one ear, or at least starts in one ear.
Since I've had this forever, I actually thought it was normal. Until I guess one day my teacher at school ran out of material, or had a hangover and just wanted us quiet. So, asked us all to be quiet and start to talk about the quietest things people could hear. Others heard a few things I could hear. Sounds in the school building. Then people were talking about hearing traffic on the street nearby and other things I just couldn't hear at all. At that point I realised, just me hearing this sound then.
I'm probably quite lucky in that the noise floor for me isn't terrible. Only at night when trying to sleep does it become a problem.