In New Zealand law, a ‘representative’ can refer to anyone acting on behalf of another person in a legal matter, while a ‘personal representative’ specifically refers to the person responsible for managing a deceased person's estate, either as an executor (if there is a will) or an administrator (if there is no will); essentially, the ‘personal representative’ is the person who handles the deceased's assets and debts according to their will or the law of intestacy. 

Key points: 

Broader application

‘Representative’ can apply to any situation where someone acts on behalf of another person in a legal process. The person acting in this role would need to establish they have the authority of the person to act on their behalf.  Presumably this would be in some form of writing.

Estate management focus

‘Personal representative’ is specifically tied to the administration of a deceased person's estate, including collecting assets, paying debts, and distributing inheritances to beneficiaries. 

Executor vs. Administrator

A ‘personal representative’ can be either an ‘executor’ (named in a will) or an ‘administrator’ (appointed by the court if there is no will).