The main issue with the descriptions is that they lack the clarity, precision and measurability of a definition. There is no reference to government or industry standards (Department of Building and Housing, BRANZ, Standards New Zealand, product manufacturers specifications and best practice publications).
They new descriptions (here for structural and here for cosmetic) are:
What is structural damage?
Structural damage refers to damage that requires an element to be removed and replaced, such as major cracking to plaster-board or external cladding that has been dislodged. It also relates to damaged foundations, roof structures and internal framing, where damage to the property is significant structural damage and could affect the overall structural integrity of the dwelling.
What is cosmetic damage?.
Cosmetic damage refers to damage that can be repaired without having to move the damaged element from its original location, such as minor cracking to plaster-board.