I don’t refer to subjective ear noise (tinnitus) - I’ve got that too.
Recently I got myself noise-cancelling headphones (type Sennheiser PCX 450), and the most noticeable change when I switch on the noise-cancelling circuit is that the noise that my own ears generate gets cancelled.
No headphones: ambient noise + (in my case) a middling tinnitus noise (steady whistle)
Closed headphones: muted ambient noise + same tinnitus noise + objective ear noise (sounds a bit like water boiling in the next room, plus a very slight heartbeat noise)
Closed headphones plus noise cancelling: still more muted ambient noise + same tinnitus noise + no objective ear noise
(my conclusion that the “water boiling in the next room” noise is objective rather than subjective is because it goes away when I switch on noise cancelling on the headphones. I also hear the noise when I stick my fingers into my ears, so it’s not an artefact of the headphones.)
So, does the sound you hear when you stick your fingers into your ears (not all the way, dummy ) sound the same?