When you're a kid and you want to go to some event or a school excursion you have to bring a document signed by your parents saying that they've given their permission. What is this document usually called?
I know it as a "permission slip".
A permission slip in the United States is a form that a school or other organization sends home with a student to a parent in which the parent provides authorization for minor children to travel under the auspices of the school or organization for some type of event, such as a field trip.
Depending on the situation, it could be a waiver if it involves agreeing to some element of risk.
A waiver is the voluntary relinquishment or surrender of some known right or privilege.
In South Africa we call it an Indemnity Form.
It the UK it depends on context and content:
Permission and consent are interchangeable to allow someone to do something. Generally permission would be to allow a minor to take part in something, consent has a slightly more formal contractual association.
Authorisation to allow someone to do some act, or incur something on your behalf.
Waiver or disclaimer if you are giving up a right (usual to claim or sue).
I always heard people around me say it as