My personal belief...every time *anyone* asks for my help and I step up to the plate, I am providing service. Doesn't matter to me if it is a colleague (internal customer), an external customer, a friend, family, or a complete stranger.
If I can do something to make your job (your life, your challenge, your issue, your breakfast) better, in that moment, for that transaction, you become my customer...no matter what the real underlying relationship is.
I spent a bit of time in production and found that scheduling is in itself a logistical challenge. Any time the production floor sends an update to the scheduler, that is customer service. One could argue that is just part of the job of the production floor. But things happen, we get caught up in the moment, and what happens if the update is never given to the scheduler? So when someone in production says, "Hey, did we ever tell scheduling that the XYZ machine broke down for four hours and we are now 1000 widgets behind?", and then someone picks up the phone and tells the scheduler...that is serving an internal customer.