Yes, and understanding the difference matters, because you may be able to pursue both. A claim on your own insurance is based on the policy you bought. It is often the first source of recovery after a fire, but it is limited by your policy limits, your coverage, and how your insurer values the loss.
A utility liability claim is entirely separate — it is against the company whose equipment caused the fire. It can seek losses beyond your policy limits, including underinsured property, the full value of your belongings, lost income, displacement, and the personal harm you and your family suffered. For many wildfire victims, this is where the fuller recovery comes from.
The two claims are coordinated: your insurer may seek reimbursement from the utility for what it paid you, which is handled as part of the process. And if your own insurer is unreasonably delaying or underpaying your claim, that can be a separate bad-faith issue. We can explain how all of these fit your situation.