To me, regular tinnitus (which I also had for a few days after concerts) could be matched and recreated with a tone generator, and is much more “in your face” despite being the same volume by the end of my ears healing.
Aether noise on the other hand sounds multi tone, not a buzz or a hum. I have not yet managed to recreate it. I can hear it all the time if I can focus on it, but it only calls attention to itself in dead silence.
Do you have visual snow by chance too?