Tinnitus is the correct spelling. Tinnitis and tinitis are two common ways to misspell it.
Exposure to loud noises can damage the inner ear, thus causing ringing in the ears and damage. The ringing in the ears is tinnitus.
With Tinitus, there are so many possible causes and cures that it is beyond the scope of this website's purpose to go into all of that (for more in depth info go to http://www.webmd.com/a-to-z-guides/ringing-in-the-ears-tinnitus-topic-overview).
So, to give a brief effective summation of ringing in ears and how it relates to TMD is more appropriate.
You can have pulsatile tinnitus which is caused by blood flowing as the heart beats. Then nonpulsatile which is caused by nerve damage or other nerve issues.
However, how it relates to TMJ symptoms is this.
When you clench or grind your teeth together, that puts pressure on the bony wall that separates the ear canal and the TMJ. This wall is very thin and the theory is that it causes inflammation fluids in the ear which causes the tinnitus. So, if you have ringing in the ears, especially in the morning after you wake up, then there is a good chance that a night guard can help reduce the ringing.
The right night guard can reduce the pressures placed in the TMJ's when the person clenches or grind teeth. So, if the night guard is adjusted correctly to reduce muscle contractions while you wear it, then any ringing in the ears caused by clenching and grinding should reduce.
Here is a link to the night guard review page. www.simpletmjtreatment.com.