Question about genealogy.

I was reading through the Evidence Bible earlier today and came across the genealogy of Christ in Matthew chapter 1. At the bottom of the page it says that the genealogy in Matthew is of Joseph, and the one in Luke chapter 3 is for Mary.
When I looked at both of them they seem to be speaking of Joseph in both of them, but they give different names between Joseph and David.
Any ideas would be appreciated.

Mat 1:16 \tAnd Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ.

Luk 3:23 \tAnd Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was [the son] of Heli,

The reason for this is that often times in the ancient world when a man married he was often listed as the son of his father-in-law in a geneaology in place of his wife. In Luke 3:23 in modern times we would read it as Joseph the son-in-law of Heli