I think Ray summarized it quite well. Fingerprints are different from DNA inasmuch as your fingerprint is not an inherited characteristic. You can't look at your parents, for example, and look at your own fingerprint and see similarities between the two.
DNA is an inheritable component passed down from parents to offspring. We look at components within the DNA, which Ray has referred to as numbers, and we can reference those numbers to the general population and see how common or how rare it is that each of the components occur. Then, by looking at a number of different components, we build up an increasingly detailed picture of the profile and address the significance of the match through the comparison to databases that tell us the frequency of the individual components or how common or rare each of the individual components is.
For fingerprints, we're simply looking at, as Ray has described, the two prints, the known and the unknown, and asking the question: are they exactly the same and do they match or not? If they match, then that's determined to be an identification. With DNA, because people are related, if two profiles match or are exactly the same, the components of the profile and how many components make up the profile will determine how rare that profile is in the general population. That can't be done with fingerprints.