Question: What does it mean to share 60% in common? How is that measured? I mean, does it not depend upon how you define commonality?
One would assume that they find common strands and then cross them out, but maybe that is not what they are doing, and maybe it depends upon the length. It would be harder to find a match if you limited the comparison to very long strings of DNA. Another thing is, the DNA strands are not the same length, so how can you use a percentage in a meaningful way?
There are many, many genes within an animal, so a 99% difference is actually quite a bit of a difference. A group of scientists actually sequenced an entire human genome and printed the sequence in books. They required several bookshelfs filled with encyclopedia-sized books to physically store only one gene sequence on paper. Keep in mind that gene sequencing isn't a complicated process; you only have four neucleobases (C, G, A, T) and unless you have a mutation they come in predictable pairs. Most of the challenge comes in size.
If something is a mammal, chances are that just because of that detail we will share a large number of genes with it. The genes that can be found across animals can form links to common ancestors. Despite the different number of chromosomes each species has (humans have 23 pairs, mice have 20 pairs, elephants have 28 pairs and mosquitoes have only 3 pairs) with gene sequencing a pattern can be seen in when comparing the genes, so to humans a banana might share a large number of genes, but given that humans have 46 chromosomes that are paired and bananas usually have 33 chromosomes that are in groups of three, comparing genes is mostly proof of evolution. However what can be helpful is when the genes compared can lead to medical advances.
The reason many heart patients can receive baboon and pig hearts instead of a human one as a replacement is because we share an overwhelming genetic similarity to those species. In fact it's a growing practice to grow transplanted organs with specific human genetic sequences (usually transmitted via a man-made non-lethal virus containing the genes) in pigs for a short amount of time so a patient's body is more likely to accept the oragan compared to just having a pig heart with similar genetics but a vastly different sequencing. The latter donor is more likely to be rejected by the body, but it's still a higher success rate compared to other animal hearts because of the similar genetics.
(You can probably tell by my answer that I really like reading about genetics.)