Plain version: the property part of a homeowners policy pays for your own things; the liability part pays when you hurt someone else or damage their things and you are legally responsible. In a homeowners policy this is Section II, which has two coverages: Personal Liability (Coverage E) and Medical Payments to Others (Coverage F).
Personal liability answers two kinds of claims:
Bodily injury (BI): harm to another person, including the medical bills and lost wages that flow from that injury.
Property damage (PD): physical injury to or destruction of tangible property that belongs to others, such as a neighbor's fence.
The test is what was harmed: a person (BI) or tangible property (PD). Being paid in dollars does not decide it. A child's hospital bill after a dog bite is a bodily injury claim, even though it is a money loss.
Dwelling policies are different. The standard dwelling forms insure property only and include no liability coverage. A dwelling owner, often a landlord, adds personal liability and medical payments with a personal liability supplement or endorsement, or buys a separate liability policy. A homeowners policy, by contrast, builds liability into Section II.