Carriers or insurance companies underwrite the risk, charge a premium, and issue policies for all types of clients. In exchange for the premium they accept a larger share of the risk and pay claims when a covered cause of loss occurs. Travelers, Chubb, Hanover, Guard, CNA, GEICO, are all insurance companies. Some of these companies sell direct to consumer or business but their main revenue comes from brokers and agents who issue polices on their behalf.
Every insurance company has a number of underwriting companies. Sometimes they are in the name of the company and many times they are legacy companies from M&A. Often they have "Fire & Casualty" in them. The underwriting companies are filed per State and determine the overall price of the premium. The better the underwriting company the lower the filed rate and the lower the premium.