From what I learned the difference is how you take your samples.
Machine capability, wich is to take into account just the machine and not the process, you take out all your samples in a row (from 30 and up is what I learned) and you do the calculations.
Process-capability, wich wants to take in the whole process (including how the operators manage the machine)m you take for example 5 products every half hour (depending on the speed of your process) and do this over a couple of hours til you have the amount of samples you want, and then do the same calculations.
Don't know if it is Swedish standard, but we usally let the machine capability give the value Cm and Cmk, while the Processcapability gives the more comon Cp and Cpk.
As for the formulas:
Cp = (UTL-LTL)/6s
UTL = Upper tolerance limit
LTL = Lower tolerance Limit
s = Sigma or standard deviation
Cpk = Minimum of [(UTL-3s)/3s;(3s-LTL)/3s)]
So in other words, the one of the 2 calculations that gives the lowest value. Hope this made sence