How David,
In IATF 16949:2016, you should consider "Customer Specific requirements" as the additional requirements for "Quality Managements System". This will include two aspects:
1)
Customer Specific Requirements" which is published in IATF website.
2) OEM's specific requirements on "supplier quality system", such as GM BIQS or QSB, VW Formel Q, Ford Q1 etc.
As for customer requirements, it is a general statement which can include everything that customer requires, like, quotation, drawing, specification, procedures...
I had no problems in the past with different certification body for ISO/TS16949.
Best Regards,
Johnson