Is building insurance the same as property insurance?

Is building insurance same as property insurance, not exactly, building insurance is part of property insurance, with property insurance broader including building, contents and liability, while building insurance covers only structure $500K to $1M. Property insurance is general term for insurance covering real property including building, contents and liability, with building insurance specific type covering dwelling structure, walls, roof, floors and permanent fixtures like kitchen, bathroom, plumbing and electrical, plus garage and shed, for $500K to $1M rebuild cost, costing $1,200 to $1,800 per year for $500K building, with $20M public liability. Contents insurance covers personal belongings $20K to $150K $300 to $800 per year for furniture, electronics and clothing. Property insurance includes both building and contents plus liability, for example home and contents insurance $1,500 to $2,500 per year for $500K building plus $80K contents. So building insurance is subset of property insurance, property insurance broader covering building, contents and liability, while building insurance only covers structure, not contents. For example, property insurance for house includes building $500K and contents $80K total $580K sum insured $1,800 per year, building alone $500K $1,500 per year. So building insurance not same as property insurance, building is part of property, property includes building, contents and liability.