Many quality practitioners treat product and process capability as if they were interchangeable concepts. Presumably, this convention has evolved over time due to the naturally strong correlation between the two. However, it would not be my recommendation to view these two concepts in the same light.
At the risk of leading a dead horse to water, we should recognize two things. First, we must distinguish the concept of “Statistical Process Control (SPC)” from that of “Statistical Process Monitoring (SPM).” In doing so, we will naturally come to understand that SPC is focused on the charting of process variables whereas SPM is focused on the charting of product variables. Parenthetically speaking, both forms of process governance use the same statistical methods and graphing conventions. Hence, the two are often spoken of in the same context even though the philosophical differences are many.
To better illustrate the nature of my objection, let us consider a product characteristic called “Y” and its corresponding process, herein known as “X”. Thus, we naturally recognize that Y = f ( X ). Consequently, we must strive to “control X” while concurrently “monitoring Y.” With all of this in mind, we must now concede that the capability of a product characteristic (Y) is dependent upon the capability of its corresponding process capability (X).
When reporting the capability of a product or process characteristic, we normally employ one or more of the four commonly accepted indices of quality performance. Of course, these indices are known as Cp, Cpk, Pp, and Ppk – each having their own statistical character and application nuances. Inherently, these indices can be applied to product characteristics as well as process variables. Unfortunately, the separation you refer to in your question is related more to application context than it is to statistical notation.