So far as I know, the wolf genome hasn’t been sequenced yet, so we can’t compare it directly to the dog genome like we can with chimps and humans. Estimates have been made, however, based on portions of the two genomes. One study compared introns and exons of fast evolving genes in wolves, dogs, and other canids. (Introns are parts that aren’t translated into proteins, exons are parts that are). They found: “Grey wolf and dog are most closely related (0.04% and 0.21% sequence divergence in nuclear exon and intron sequences, respectively), followed by a close affiliation with coyote, golden jackal and Ethiopian wolf, three species that can hybridize with dogs in the wild”. http://www.nature.com/nature/journal/v438/n7069/pdf/nature04338.pdf (p. 815). Compare that 0.04% to 0.21% in fast-evolving genes with the distance between chimps and humans, which is roughly 2.5% to 6%, (depending on exactly how the differences are measured) across the entire genome, including both fast-evolving and slow-evolving regions. Clearly dogs and wolves are much more closely related.
Another important difference is that dogs almost certainly evolved from wolves, whereas humans probably did not evolve from chimps. Instead humans and chimps likely evolved from a common ancestor that was neither human nor chimp. In your linked question, Rick in the Santa Hat says that a wolf didn’t give birth to a dog. That’s true, because the characteristics that are indicative of dogs built up little by little over many generations in the lineage leading to dogs. So there would have been many generations during which it wouldn’t be clear whether the individuals in the populations were wolves or dogs. Rick goes on to say, however, that “Chimps and humans share a common ancestor, and modern wolves and dogs share a common ancestor.” That overlooks the fact that the common ancestor of wolves and dogs was a wolf, while the common ancestor of chimps and humans probably wasn’t a chimp.
I say “probably” because we don’t actually know what the likely common ancestor of humans and chimps looked like, nor do we have fossils of chimp precursors. So far as I know, it therefore remains theoretically possible that we did evolve from chimps. Chimps live in the jungle where fossils rarely form. By comparison, we have fossils of wolves predating the earliest dog fossils, and we have fossils that appear somewhat intermediate between dogs and wolves.
As for why chimps and humans can’t produce offspring, how do you know they can’t? Very few attempts have ever been documented (as one might imagine given the ethical considerations regarding any children produced). Assuming they can’t produce offspring, the reason would not be that they have a different number of chromosomes. The Eagle Lake rainbow trout hybridizes easily with other rainbow trout despite the fact that it has 58 chromosomes instead of the normal 60. Similarly, we have 46 chromosomes instead of the chimp’s 48. One of our chromosomes (chromosome 2) is analogous to 2 of the chimp’s, so during meiosis the two chimp chromosomes would simply line up opposite the single analogous human chromosome. So if we can’t interbreed it would be because the two species have evolved independently to the point where some of the proteins or activation sites in one species can’t interact appropriately with proteins or activation sites in the other species. The chances of that happening increase over time, and also increase if hybrids would tend to be poorly adapted to the habitat in which they were born.
Richard Dawkins provides a great overview of the genetic links between humans and chimps here: http://www.animal-rights-library.com/texts-m/dawkins01.pdf Here’s a sample:
“Happenings are sometimes organised at which thousands of people hold hands and form a human chain, say from coast to coast of the United States, in aid of some cause or charity. Let us imagine setting one up along the equator, across the width of our home continent of Africa. It is a special kind of chain, involving parents and children, and we will have to play tricks with time in order to imagine it. You stand on the shore of the Indian Ocean in southern Somalia, facing north, and in your left hand you hold the right hand of your mother. In turn she holds the hand of her mother, your grandmother. Your grandmother holds her mother's hand, and so on. The chain wends its way up the beach, into the arid scrubland and westwards on towards the Kenya border.
How far do we have to go until we reach our common ancestor with the chimpanzees? It is a surprisingly short way. Allowing one yard per person, we arrive at the ancestor we share with chimpanzees in under 300 miles. We have hardly started to cross the continent; we are still not half way to the Great Rift Valley. The ancestor is standing well to the east of Mount Kenya, and holding in her hand an entire chain of her lineal descendants, culminating in you standing on the Somali beach."