Indemnity is basically when one person has to pay for the loss of another. Indemnity may be based on either contract or fault.
Insurance companies that agree to pay for a loss are agreeing to indemnify their insured for some loss. This is a form of contractual indemnity. Another form is contracts between parties which state that one party agrees to indemnify the other for losses arising from the contract or the work.
Equitable indemnity arises from fault. As Bernard Witkin said in Summary of California Law (& quoted in Sammer v. Ball, 12 Cal.App.3d 607 (1970): “To a person who without fault has been compelled by reason of some legal obligation to pay damages occasioned by the initial negligence of another . . . the right of indemnity enures.”