These terms mean something very specific in the Quality field.
The word "capable" means if the process is stable, it will yield adequate results. Variability is the most important issue. For example, if specifications specify a variance of of 2 or less and the process has a variance of 4, we know there no use in attempting to use this process. In this case, we say the process is not capable. An engineer that tries to use the process by adjusting the set point is in for a great deal of frustration!
Even the phrase "Meets the requirements" is not as simple as it seems. The question is: whose requirements? This may be part of a Quality Function Deployment discussion. This phrase could also be a part of a discussion concerning "fitness for use", which is a Juran concept.
I hope this puts you in the right direction!
Best wishes,
Tom