The customer is the end purchaser and user of insurance products. Once insurance has been purchased and cover is in place, they become known as "the insured".
The basis for the relationship between the insurer/underwriter and the customer is the insurance contract. In most cases this comprises the policy wording and the policy schedule.
The insurance contract is essentially a promise made by the insurer that, if the "risk" covered by the policy should occur and a claim is made by the insured, then the insurer will cover or "indemnify" that insured against the particular risk (provided that the insured has paid the required premium, met all obligations it may have under the policy and the claim falls within the scope of cover provided by the policy).
In the context of commercial insurance products, the insured customer shown on the diagram of the insurance industry would be more likely to be a company rather than an individual.