The National Cancer Institute provides funding for research. Institutions apply for NCI designation (the selection is done through a peer-review process), and the term "NCI-designated" primarily has to do with the facility's research interests --- not the quality or scope of patient care.
An NCI-designated comprehensive cancer center means that the institution is involved in research in three areas: laboratory, clinical and population-based. All NCI-designated comprehensive cancer centers also treat patients. An NCI-designated cancer center concentrates research in one or two of those areas, and a few of these facilities -- like the Wistar Institute in Philadelphia or the Salk Institute in San Diego -- do research only. Further information is available here:
http://www3.cancer.gov/cancercenters/description.html By contrast (and Brian or Gary, please correct me if I am wrong), the term CCC as most frequently used here means that the facility uses a team approach to dealing with an individual case, bringing the knowledge and experience from a variety of specialties to each treatment plan -- a "comprehensive" approach, as it were.
Stanford is part of the National Comprehensive Cancer Network (NCCN), an alliance of 20 of the leading cancer centers across the United States. The NCCN's focus is primarily on patient care and clinical practice guidelines. Here is information about that network --
http://www.nccn.org/about/default.asp -- Leslie