In the states with no-fault insurance, insured drivers are typically paid for medical expenses by their own insurers, regardless of who caused the accident. Nonetheless, BI liability coverage is still required in no-fault states because if injuries are bad, the at-fault driver may be sued by the injured party. If that happens, your BI coverage can help cover your liability expenses.
Collision coverage is generally sold with a separate deductible. Even if you are at fault for the accident, your collision coverage will reimburse you for the costs of repairing your car, minus the deductible. If you're not at fault, your insurance company may try to recover the amount they paid you from the other driver’s insurance company and, if they are successful, you'll also be reimbursed for the deductible.