It sounds as if you are comparing the same object to itself. Obviously the sound is the problem and our label for the sound is the word "tinnitus". So, asking if it's tinnitus "or the sound" is a bit off. That's like saying, "Is cancer really the problem, or is it the abnormal growth of cells?"
To dive a little deeper, I'd say the biggest problem with tinnitus (which is the sound I hear) is the type of sound. If we all heard relaxing music, this site probably wouldn't exist. But, the fact that the noise, that under normal circumstances, triggers your limbic system to warn you of an impending threat is the real issue. You hear many sounds every day that you don't even notice because they don't register as "dangerous".
My personal theory in habituating to tinnitus revolves around the questions: How can I tell my limbic system that tinnitus is not something it needs to warn me about? How can I tell my limbic system to go back looking for other threats? Well, obviously the limbic system does not take commands in the form of human language. You can't say - "Hey, ignore that sound." Therefore, I've determined that you "speak" to those areas of your brain through a action/reaction method. Meaning, the more you react to something, the more your limbic system is reinforced that the stimulus is important enough to freak out about. The more you under-react... over time sends a message that the stimulus is not very important. So, how do you under react? That amazing tool called the prefrontal cortex. This is where you make a conscious decision about how to respond and you don't allow your brain to push the panic button.
For example, if you were afraid of spiders and the sight of one caused you to freak out and panic, then expect the same response every time you see a spider. Eventually, your reaction could spark full-blown panic and you could live in a state of fear - never wanting to leave your house because you may see a spider. Afraid to sleep because of spiders. But, what if the next time it happens, you decide you are going to stop, take a deep breath, relax, and handle the situation differently? Instead of a panic reaction, you respond deliberately and consciously. Well, over time... your reaction to spiders would change. With enough practice, your limbic response to seeing a spider would be minimal. How does this relate to tinnitus? I like to say... ironically enough... "The more you can live without tinnitus, the more you live without tinnitus." It's easy to get worked up and to think - I will have to hear this noise 24/7 the rest of my life!!! But, that's sort of lying to yourself because nobody really hears it 24/7. We all have times throughout our day in which we are unaware of its existence for several reasons. So, let's not give it more credit than it deserves and lets empower ourselves by acknowledging that it is not 24/7. The next question to ask yourself is - how many hours a day do I notice my tinnitus? Maybe 12? 4? 8? 2? Whatever the number is, the goal is to use techniques to reduce it over time... and you reduce it by taking your brain's attention away from it by doing whatever you can: call a friend, turn on the TV, listen to some music, meditate on your breath, sing, etc.... because all of these things contribute to the same purpose - blunting the warning from the limbic system. Essentially, you are speaking to it... sending the message... "This sound is not important. I do not care about it." Hence... the more time in your day you can spend not fixated on your tinnitus, the more you live without tinnitus.
Anyway... I'm not a doctor, so maybe I'm wrong. But, that's just my summarized, casual, observation. It has worked for me.