The latter has to do with handling specific losses (see below), the former is just the plain process of dealing with a claim starting with its investigation and concluding with its settlement or disposal. This work can be carried out by an insurer's own claims staff or by a loss adjuster (= a highly trained and independent claims expert engaged by insurers to investigate claims and assess the true extent and value of any loss; he is not engaged for smaller, routine type losses).
The "average adjustment" idea, on the other hand, would be corroborated by the dictionary no. 2 referred to below where "komisarz awaryjny" = "average surveyor, average agent" (marine insurance). Dictionary no. 1, however, only contains "average ADJUSTER" who, indeed, handles marine claims, although "average" as such is a term also used in non-marine insurance to describe a device to penalise and deter under-insurance.
So, if your "komisarka awaryjna" has nothing to do with marine insurance or chasing under-insurance, I would opt for the plain "claims adjustment"

Hope this helps,
Jacek Krankowski