Both types of tests look at the same DNA, but NCI's testing won't give you the information you need for genealogical purposes, and the testing services that market to consumers aren't allowed to give you the kind of health-related information that NCI will provide. So if you want DNA data for genealogical purposes, you will also need to test with a consumer-oriented service.
I think 23andMe is the only testing service for consumers that includes a significant amount of health-related information, in addition to data that can be used to understand ancestry. I tested at 23andMe before the U.S. Food and Drug Administration (FDA) told them to stop giving health-related information to their customers. For customers who opted in (customers had to opt in to get potentially bad news about genes related to breast cancer, Alzheimer's, and possibly also Parkinson's disease), 23andMe gave data on the major BRCA1 and BRCA2 mutations and some other genes with some relationship to breast cancer, but warned that their tests did not look for some other mutations that affect the genetic component of breast cancer risk. (Now that 23andMe has FDA approval to report some health-related information, I don't think BRCA mutations are on the list of what they are allowed to report.) I expect that NCI testing looks for all of those other known or suspected breast-cancer-related mutations. So you are getting some tests that you can't get from a consumer service, but you'll need to test with a consumer service to get genealogically useful DNA info.