What's the difference between control limits and specifications?

While covering the topic of control charts for process control in SPC training, I always get very interesting questions.
One of my favorite's is "So, what's the difference between control limits and specifications?"

But in the SPC training I did last week, this one student went to the extent of saying that it is misleading that points out of control limits on the control charts signal problem when there is no problem at all...my parts are within specifications and are good to be shipped to my customer.
I patiently explained what control limits are, how they are calculated and what an out of control point means.
However, this student was just not getting it and was confusing all the other students too. I was surprised when the Quality Manager jumped in the discussion and actually supported this woman who worked in the Quality department for years at this company.

Both of them kinda challenged the basics of control charts and were tending to prove that control limits are not needed on control charts. Instead specification limits should be used.

I explained the difference between control limits and specifications again. Only this time I introduced pre control charts. A comparison of pre control with control charts seemed to make sense to the Quality people.

The use of control charts for identifying special causes in the process and removing them does not seem as important as producing parts that are out of specifications. Sad, but true!
These days, the concept of having a stable process that produces good parts seems to be lost.