DNA fingerprinting refers to :-

DNA fingerprinting (DNA profiling), developed by Alec Jeffreys, compares the DNA of individuals by studying highly variable regions called VNTRs (variable number tandem repeats) or satellite DNA.
The DNA is cut with restriction enzymes, the fragments are separated by electrophoresis, blotted, and hybridised with labelled VNTR probes (Southern blotting). The resulting band pattern is the DNA profile.
Each person (except identical twins) has a unique pattern, so it is used in forensics, paternity disputes and studies of populations.
It has nothing to do with the fingerprints on the fingers; the name only means that the pattern is as unique as a fingerprint.
So DNA fingerprinting refers to the molecular analysis of profiles of DNA samples.