I have attended a couple of webinars and read a couple of books which makes me in no way an expert. This Guide to DNA Testing by Richard Hill, who is an expert, was the clearest explanation that I have read.
My very brief summary, and feel free to comment if you know better, is that there are 3 major kinds of tests.
Father’s Line – The Y chromosome test can determine if men are direct descendants of the same ancestor. This would be useful for determining if the Édes men I have met are really descended from the same family who settled in Madár in the 17th century.
Mother’s Line – Only women pass down mitochondrial DNA to their children. This test is used for confirming direct maternal line relationships between women. Not as commonly used as the other tests.
Cousin Finder – The basic are-we-related? test. Autosomal DNA can be used to find relatives within up to 5 generations. The other reason for this test is to learn about your ethnic background and ancestry. I am starting with this one. I don’t really expect to find any relatives, although that could be fun. But I am interested to see if the background results match the family stories.