I came across terrific online explanations of DNA from the University of Utah. The short videos plainly explain four types of genetic inheritance: autosomal, X chromosome, Y chromosome, and mitochondrial DNA, and their applicability to genealogical research.
The testing that I write about from 23andMe is autosomal. The kit that I ordered from Ancestry a few days ago is autosomal testing. The surname projects at FamilyTreeDNA (which I have not done yet) are Y chromosome DNA testing.