Science behind the mitochondrial DNA test
Mitochondrial DNA test is based on the circular DNA present outside the nucleus of a cell. This test is very useful when nuclear DNA (nDNA) test is not an option. This test makes use of variations present in the mtDNA and is assessed through sequencing rather than fingerprinting. Men (males) inherit mitochondrial DNA (mtDNA) from their mother but do not pass it on to their offspring. On the other hand males inherit Y-DNA from their father and pass on Y-DNA to their sons only. This test however, can not tell you the nature of relationship between the tested parties.
Maternity DNA Test vs mitochondrial DNA test
A maternity test can confirm the biological relationship between a child and mother by comparing the DNA profiles of the two. Mitochondrial DNA on the other hand can determine whether the tested parties share a common maternal lineage.