Homeowners insurance protects your home and belongings against sudden, accidental events - fire, windstorms, hail, theft, some water damage - and covers liability if someone is hurt on your property. A home warranty is a service contract that repairs or replaces covered systems and appliances when they fail from normal wear and tear.
Put simply: if a storm destroys your AC unit, that's an insurance question. If your AC unit simply wears out, that's a warranty question.