There seems to be a certain amount of spread in the terminology here (pun intended).

I assume that only one coefficient is meant here, namely Cpk (a term from machine capability and process capability analysis).

At least one source (ref. 1) calls Cpk the 'process capability'. Arguably it could be called the 'process spread and centering coefficient index' (as a more or less literal translation of the German). However, another source (ref. 2), which deals with the related concept of machine capability, calls the same term the 'centering coefficient' or 'centering index'.

Ref. 1:
http://www.st.com/stonline/press/news/glossary/c.htm

Cp
Capability index
The capability index indicates the relationship between the product's specification (planned tolerances) and the process capability or spread (natural tolerance of the production process). The process has to be in statistical control, i.e. only common causes of variation are present.

Cpk
Process capability
When a process is in statistical control we need to measure its ability or fitness for meeting a specification. A good measurement is Cpk: it takes into account both centering and dispersion (accuracy and precision). When both the Cp and Cpk have the same value, it indicates that the process is centered with the nominal value of the product specification. This is the optimum condition. When the process suffers from the effect of variables which drift in time, and it is no longer centered with the nominal value of the product, it is useful to know the value of Cpk. While the value of Cp may remain unchanged, the value of Cpk may vary.
The Cpk calculated with the data obtained from a process provides the measure of the performance of that process.

Ref. 2:
http://www.smtnet.com/express/200303/machine/

Thus, machine capability coefficients are calculated as follows:
Cp = [expression] (Spread)
Cpk = min(expression) (Centering)

Cp, Cpk: Machine capability indices
USL: Upper Specification Limit
LSL: Lower Specification Limit
X: Mean
s : Standard deviation

[where 'expression' indicates a mathematical expression that doesn't copy to here]

Ref. 3:
http://www.moresteam.com/glossarynewprint.cfm

Cp A measure of potential process capability. Cp is the ratio of the six-sigma spread of a process distribution to the tolerance of that distribution. The process must be stable (in control) in order to assess Cp. Cp is calculated without accounting for the centering of the process. If the process is centered exactly in the middle of the tolerance, Cp is exactly equal to the maximum capability (Cpk).

Cpk A measure of the actual process capability after taking into account the centering of the process. It is calculated by dividing the distance of the process mean to the nearest tolerance limit by 3 standard deviations of the process. The process must be in control before assessing Cpk.

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Note added at 7 hrs 18 mins (2004-12-07 21:47:31 GMT)
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Correction: in the third paragraph, that should be \'...spread and centering coefficient/index\'