Two minute introduction: life is largely built out of proteins, which are chains of amino acids (small organic molecules) which "fold" into interesting shapes and interact with each other in interesting ways. Our DNA is a set of blueprints for making a suite of proteins that builds us.

One of the curiosities in our DNA is that multiple sequences can code for the same amino acid in a protein. It doesn't matter how it's coded in your DNA, the protein still functions the same way. So one piece of evidence in favor of evolution is that most organisms share a common DNA sequence for common proteins, even though there are potentially millions (or more!) of different sequences which would code for the same protein.

So if humans and pigs have evolved any of the same proteins since they diverged millions of years ago, you should also expect them to be coded for in "more different" ways than if they were evolved in a common ancestor.

(You wouldn't expect the coding for the proteins to be completely different, since they probably evolved from a protein shared by the common ancestors.)