DNA fingerprinting is generally done with STRP short tandem repeat polymorphisms.
I imagine SNPs would be used to determine differences in certain alleles.
From wiki: "The nucleotide diversity between humans is about 0.1%"
Our genome is ~3 billion basepairs, 0.1% of 3 billion is 3 000 000. SO between any 2 people there is said to be ~3 million nucleotide differences!