Autosomal DNA vs. YDNA and MtDNA Tests

 I was trying to explain to a cousin why a man taking a DNA test from FamilyTreeDNA would fail to find any matches with his maternal surnames. This is what I came up with.

Much depends on the type of DNA test. 
In my experience, FTDNA tests are usually limited to the 23rd chromosome pair, either YDNA or MtDNA.
So any matches would be limited to the direct paternal or direct maternal line exclusively.
Whereas Ancestry, MyHeritage, 23&Me, etc. use autosomal tests, based on all of the other chromosomes.

I have a little involvement with the Buchanan YDNA project at FTDNA, and more involvement with AncestryDNA  through a cousin I have been helping. But I am by no means an expert on the subject.

An Andrews man who took a YDNA test should see matches with men named Andrews but not with men named Hamilton or Buchanan.

If the same man took an autosomal test, he should see matches with men and women named Andrews, Hamilton, and Buchanan. (i.e. people related on all family lines)  

Presently, AncestryDNA has the most subscribers, so the largest number of potential matches.

Autosomal tests tend to be much cheaper, but their accuracy it usually limited to 5 or 6 generations. The other tests are accurate much further back, but only follow one family line.

I hope this helps.

Bill