For mortgage transactions, the lender requests the appraisal, either directly or through a third party.
Even though it’s the buyer that eventually pays for the report, the lender is the intended user. The buyer is entitled to a copy of the report – it’s usually included with all the other closing documents – but is not allowed to use the report for any other purpose without permission from the lender. It’s different when it’s the homeowner hiring the appraiser for things outside securing a mortgage.
In these situations, the appraiser may state the purpose of the appraisal; for PMI removal, or estate planning or tax appeal, for example. If not noted otherwise, the home owner can do whatever they want with the appraisal.