(a) there is a requirement in the contract that you should follow this standard,
(b) there is no mentioning of this, but cited that one should follow generally accepted practice in the industry, applicable standards, etc. (a vague reference to compliance with the applicable "rules"), and
(c) if nothing is said at all (could this AITF-standard possibly be considered as future industry practice?).
How specific are the demands of those who will need to follow the IATF standard? May I ask for any illustration about this? Is the standard just about to keep order and stay organized in general or is there more specific requirements that are measurable and can more easily be said to violate?
It would also be interesting to know if there is any supervisory body and if there are any sanctions if you do not do what is required.
Implementation of the standard is not mandatory in sense of legal requirement, but if the customer requires it, you should implement it in order to keep the customer. The standard itself requires from the organization to require either IATF 16949 or ISO 9001 from its suppliers, so ISO 9001 is very minimum required from the companies supplying the IATF 16949 certified companies.
The standard represents the set of rules and best practices in the industry and covers all processes related to the manufacturing of the product, as well as requirements for continual improvement. Most of the requirements are general because they should apply to different types of industries and different types of companies and the requirements are in most cases regarding the organization and managing the processes. For more information, see: What is IATF 16949? https://advisera.com/16949academy/what-is-iatf-16949/
There is a supervisory body, and it is called certification body. You can hire them to audit your system and issue you a certificate to testify that you are compliant with the standard. In case when there are nonconformities found during the certification audit, you will get a report about the nonconformities and once you remove the nonconformities, you will get the certificate. For more information, see: Checklist of IATF 16949:2016 implementation steps https://advisera.com/16949academy/knowledgebase/checklist-of-iatf-16949-2016-implementation-steps/