I don’t really know what a ‘management expert’ is. Not a common phrase.
An auditor’s expert is someone who gives independent expert opinion to an auditor. For example, an estate agent on the valuation of buildings. The auditor needs expert help in such an area because most auditors will know little about property values. This expert must be independent of the client so, for example, could not be an estate agent regularly used by the client on the purchase and sale of property.