The name SRS for a "software requirements specification" is well established and depending on how it's understood it could be written by the customer or written by the supplier. Colloquially, both "requirements" and "specification" are regularly used to refer to such document. It is similar to calling a document that describes test instructions either a "test specification" or a "test procedure" -- different people/projects/companies, different conventions.

What matters is to have a common understanding and work together.