No, that isn't correct. A deer hit is covered under comprehensive and someone without any insurance or enough insurance is covered under uninsured or underinsured motorist, respectively. Most people misunderstand "no fault". No fault refers to coverage for your medical bills if you're injured in the accident. In a no fault state, you go to your own insurance carrier for medical bills regardless of who's at fault for the accident. In many of the no fault states, the insurance carrier cannot recover those medical bills paid even if their driver isn't at fault. Even in a state that's not "no fault", the at fault insurance company still won't pay your medical bills up front. You handle them through your own carrier, your private insurance, work comp, whatever. When you're done treating, the at fault will gather all medical bills and records and settle the claim then.
Every state has liability laws. They vary state to state. In some states, you recover the exact amount the other party is at fault. So if you are 15% at fault, you recover 85% of your damages from the other company, the other person can collect 15% of their from your carrier. Other states bar you from recovery if you are 50 or 51% at fault. Some states bar you from any recovery if you are 1% at fault. By the way, the police don't make that liability determination, the insurance company does. Michigan is the only state that varies from these. For the most part, you go to your own insurance company regardless of who is at fault or how much. It's complicated, but that's the upshot.