Adjustor was a legal title like attorney at law when I was hired by a major commercial lines insurance group in 1970. I was the first Adustor in their 100 year history who was not a law school grad. I was a psychology/history double major, but also a math/physics prodigy capable of complex abstract analysis which applied to many areas. The term "aduster" was applied to college grads (usually) who worked for primarily personal lines insurance companies, were also given company cars and expense accounts, with emphasis on a lot of training in property damage estimation and understanding of specifics of insurance policy coverages regarding farmers, homeowners, smaller businesses, and vehicle coverages. In addition to those types of claims, I was heavily used for forensic reconstruction of multi vehicle and fatality accidents, serious product liability cases, medical malpractice defense, embezzlement cases worked with local detectives and FBI agents, and a lot of collaboration with scientists and legal experts at the University of Note Dame for three years before moving back to Southern California.
Both terms apply to an agent of a licensed insurance organization who had authority to fully represent, negotiate and bind the organization to settlement contracts. The average adjuster I knew had $1,500 draft (corporate check) authority and $5,000 tentative settlement authority. In my second year I was authorized to sign drafts for up to and including $50,000, and confirm settlements up to $500,000.
I have not noticed any use of the term "Adjustor" for thirty years, but "insurance adjuster" is common for independent adjusting firms. Insurance firms commonly use something like "Field Claims Representative" for the same function. I suspect that the original was Adjustor, dating back to the 19th Century. Hope this helps, if anyone's still there.