Yes, there is a difference between saying someone is liable and someone negligent.

If you are liable, you are obligated by law or equity. If you are negligent, you are at fault or not exercising the care expected of a reasonably prudent person in the same situation.

A person must use reasonable care in driving a vehicle. Drivers must keep a lookout for pedestrians, obstacles, and other vehicles. They must also control the speed and movement of their vehicles. The failure to use reasonable care in driving a vehicle is considered negligence.

Determining if the Liability portion of an insurance policy will pay for a claim is specific to each individual claim. Typically the party would be negligent in order to be liable for their actions under the law, but a Liability policy could pay out even when the insured is not negligent, but that is not typical and would be argued.

An insurer will pay out if they find you are liable for an accident due to negligence they found on your part. If it is found that negligence that caused an accident such as running a red light, following too closely, etc than they would find you liable and thus your Liability coverages would pay out to those your harmed.

While if a person with no known medical conditions unexpectedly has a stroke and is unable to control their car and crashes into another vehicle it may first appear that that driver was negligent however once the medical reason for the loss of control is found out an insurance company will normally deny there being liability on the part of their insured since there was no negligence and so deny a claim. In this case if the stroke was truly unforeseen, and the driver was not otherwise operating the vehicle in a negligent manner, then there is no negligence and so according to the terms of most auto insurance policies no liability.