Fault definitely matters!
In terms of who pays your medical bills, Florida is a no fault state and your own insurance pays your medical bills, regardless of whether you are at fault or not. That is the no fault laws in Florida.
Now, in terms of who pays to fix the car, we are on a fault system. So if another person causes the accident, their property damage insurance coverage (which happens to also be required) will pay to fix your car if they are at fault.
Lastly, in terms of who pays you for your injuries (unpaid medical bills AFTER PIP, pain and suffering, etc.) we are also on a fault system. Thus, if the other car is at fault their bodily injury coverage (which is generally not required) will pay you for your injuries.