well the automtive world (AIAG) isn't the only industry out there...
actually in your table both GM and Ford have the correct naming convention from when Ppk was introduced. (in the beginning there was only Cp/Cpk and it didn't specify a standard deviation - the original assumed it was the total standard deviation and not the within subgroup standard deviation. In a homogenous stable process the within subgroup variation is a decent estimator of the total SD)
Cp stood for Process capability: Capability_process and Cpk stood for Process Capability in real life. the k was the offset of the mean from the nominal.
Then someone got cute and added Ppk to mean Process_Performance (long term) and Cpk to mean Process_Capability (short term) - now GM and Ford both refer to these descriptor 'correctly'.
The phrase Short term refers to the use of the withing subgroup variation , which in a classical Shewhart chart of a homogenous, stable process is very short term.
Long term refers to the use of the total standard deviation which can be a very long time - from subgroup to subgroup.
this was articulated directly by the Six Sigma folks at Motorola. GE and other companies also have referred to Cpk as short term and Ppk as long term.
Most statistical software uses this designation.
Then Ford got cuter and decided that neither adequately addressed the need for protype or preproduction analysis when there was only one lot, operator, equipment, raw material lot, and it was alimited build run. so they used the 'Ppk formula' to calculate the short term capability when there was no subgrouping.
The original article (unless someone knows of an earlier article?) introducing capability indices is: "Reducing Variability - A New Approach to Quality", Quality Progress, July 1984.
I also recommend reading the October 1992 issue of the Journal for Quality Technology devoted entirely - and reluctantly - to the topic. The intent was to deal with this 'fake' statistical index and kill it from serious consideration by serious Quality and statistical professionals. The January 2002 issue also contains some review of indices since the 1992 publication as well as an article and discussion regarding the Cpk/Ppk confusion and other problems with the indices.
And no one did it better than Bert Gunter in his 4 part column: The Use and Abuse of Cpk" in Quality Progress January, March, MAy and July 1989
Recommending what to call them is as futile as admonitions to just say no.