Stable Process is a process where the observed variation is largely within the control limits or in other words almost all of the observed variation is the Common Cause variation. There are minimal assignable causes of variation in a stable process. A stable process will rarely have outliers or unusual output values.
Capable Process is a process where the observed variation is largely within the specification limits or in other words has minimal rejections. Such a process almost always produces as per customer requirements.
An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Manjeet on 11th January 2019.
Applause for all the respondents - Prashanth, Vastupal, Vipul, Mathi and Devesh
Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.