An "indemnity" policy will not pay claims until the insured has paid out of pocket to some third party; i.e. a visitor to your local slips on a downstairs that you left dripping and Health Insurance sues you for $10,000 and wins. Under an "indemnity" policy the homeowner would have to come up with the $10,000 to pay for the visitors decrease and then would be "indemnified" by the cover carrier for the out of pocket costs (the $10,000).
Guidance exists for insurers and reinsurers, whose CEO's and CFO's attest annually as to the reinsurance agreements their firms undertake. The American Academy of Actuaries, for instance, identifies three categories of contract as outside the requirement of attestation: