Hearing loss is a physical problem. Tinnitus, often, is a signaling problem. The signal can represent a sound that the physical sensors can't produce anymore.
It's a fair question, and it's hard to describe. What I perceive is a very high pitched pure sine wave. When I take a hearing test, my ability to hear real tones drops off long before I can hear anything approaching the pitch that I perceive. Does that make sense?
It’s two different sources, and a subjective tinnitus source is perceived but not “heard”, if that makes sense. You might be able to experience something perhaps similar: many people can hear much higher frequencies when the speaker is in contact with their skull than through the air.
You're not actually "hearing" anything. For one, the sound (usually) does not actually exist. In many cases it's more like an inappropriate signal from a damaged nerve or some of the teeny tiny "hairs" within the ear that sense sounds.