Like the other posters already said, a customer is a customer regardless if it is internal or external.
Oh, if only it were that easy to interpret 9000 and 9001! There is often a gap between what folk think of as their organisation's "customers" and "products" and what the definitions in the standards seem to say. ISO9000 says that: "a customer is an organization or person that receives a product (ie the result of a process)", but a note in ISO9000:2000 states that the term “product” applies “only to the product intended for, or required by, a customer”. [Of course it is - it is part of a circular definition!]
Although the concept of “internal” as well as external customers does give a useful reminder that individuals within the organisation rely on others’ performances, I believe that the way most people think of the term “product” is still largely used in relation to the “deliverable” supplied by the organisation to an outside party (an external customer).
If customers can be internal, the term "customer-related processes" is a tautology - by definition, every process must be "customer-related". Confusing?
It gets worse: 3.5.2.3 defines a "service" as "intangible product that is the result of interaction between customer and supplier", and NOTE 2 then totally confuses me by talking about "the product of a service..." (ie not of a process)... And the fact that "product" is defined as "the result of a process" is then compromised by the term "product realization processes" which implies that other processes don't "realise" (ie create) products.
3.10.1 NOTE 2 says that "External audits include those generally termed second- and third-party audits. Second-party audits are conducted by parties having an interest in the organization, such as customers..." which sounds very much to me as though they are external to the organisation.
And ISO9001:2008 has complicated it further by saying that "In this International Standard, the term “product” applies to the product intended for, or required by, a customer or the product realization processes. This applies to any intended output resulting from product realization processes, including purchasing". Surely there must be a simpler way to define and explain the basic terms that everyone uses?
I am well aware of it. The OP mentioned it in the forum title and the posting. Any reason for you reminding me that?
However, an organization lives by the entity bringing in the cash; the external customer. I would be most concerned about them.