Who pays the adjuster is the fact that organizes everything else. A staff adjuster is an employee of the insurance company. An independent adjuster is a contractor the insurance company retains, often to absorb a surge of claims after a catastrophe or to cover territory where the insurer has no staff. In both cases the person inspecting your kitchen is being paid by the party that will write the check. That is not a scandal and it does not make the estimate wrong; insurers have a regulated obligation to investigate claims reasonably, which published material on the claim process covers. It does mean the number in the estimate is one side's valuation, arrived at by that side's methods, and a policyholder who treats it as an objective measurement has misunderstood what document they are holding.
Licensing reaches less far than most people assume, and the gap is deliberate. California's Insurance Adjuster Act, at Insurance Code sections 14000 through 14099, makes it unlawful to "engage in a business regulated by this chapter, or act or assume to act as, or represent themselves to be, a licensee" without a license, and section 14021 defines an insurance adjuster as a person who, for any consideration, investigates in the course of adjusting or otherwise disposing of a claim on behalf of an insurer. But section 14022 exempts "a person employed exclusively and regularly by one employer in connection with the affairs of the employer only" where an employer-employee relationship exists. The practical effect is that the Act licenses the contractor and not the insurer's own employee. Requirements differ by state, so this is California's line rather than a national rule, but it is the shape of the question worth asking: an adjuster is not necessarily licensed simply because they are adjusting.
The same statute anticipates the two things that go wrong in a long claim. First, adjusters change hands. California requires that where an insurer assigns "a third or subsequent adjuster to be primarily responsible for a claim" within a six-month period, it must give the insured a written status report summarizing the decisions and actions substantially related to the claim's disposition, including the amounts of loss to structures and contents and all items in dispute. That provision exists because a claim passed between four people loses its own history, and the burden of reconstructing it otherwise falls on the policyholder. Second, the same section requires the insurer to tell every claimant that they may request copies of "claim-related documents," a defined category that includes repair and replacement estimates and bids, appraisals, scopes of loss, drawings, plans, third-party findings, and the insurer's own loss-adjustment calculations, and to provide them within fifteen calendar days of a request. Attorney work product, privileged documents, medically privileged information and documents indicating fraud are excluded. Asking for the file is a defined right in that state rather than a favor.
After a declared disaster the licensing picture changes again. California's emergency provision requires a licensee or qualified manager supervising nonlicensed adjusters to ensure each of them reads the insurance department's most recent notice and adjuster handbook within fifteen calendar days of beginning claims-adjusting activity in the state. That rule exists because catastrophe surges are staffed quickly, which is exactly when a policyholder is least able to tell an experienced adjuster from a new one.
A public adjuster is the mirror image and is regulated separately. The point to carry away here is only that the category exists and that its economics are the reverse of the other two: the policyholder engages and pays the person, so the incentive runs the other way. The detail belongs on its own page.