How do we define the concepts specific activity, radioactive concentration, carrier, carrier-free and no-carrier-added?

In nuclear and radiochemistry the concepts of specific activity, radioactive concentration, carrier, carrier-free, and no-carrier-added play important roles. It turns out that these concepts involve various - and sometimes conflicting - interpretations and definitions. The most recent IUPAC recommendations on these concepts will be given and discussed as to their correctness, relevance, clarity, and consistency. On basis of this discussion, tentative suggestions will be given for revised definitions of the concepts listed.