50% chromosomal rearrangements between rats and mice. A lot less in the primate lineage. Correlated to why the jump between species for AIDS was so easy? Definitely.
Retro viruses have a high mutation rate, thus why they are hard to treat. We already have cures for such retro viruses as involved with AIDS but the problem is it would only kill 10% of them (as that is the faction of the retrovirus the cure works on due to rapid mutations) and quickly diminish down to 0. Even with a whole battery of cures for retro viruses, it can only hammer like atmost 50% of them as there are so many different kinds. The reduction is not enough to make any difference and after 1 application the effectiveness will drop to 0. Thus why there is currently no cure for the whole condition and no one botheres to work on curing specific retro viruses.
With enough exposure to something that is mutating that much, it is almost garunteed that humans will eventually get it. The problem with AIDS is not the concept behind it, as we have had retro viruses attack our immune system since humanity existed, but the way it does. Unlike human AIDS which is completly harmless to us (it was not even documented until recently as it farnkly does nothing), this was AIDS from another species that mutated slightly to be able to affect us. As such, most of humanity is suceptable to this form of attack without retaliation as it is just not recognized. There are even doubts it did cross the species barrier as older and older cases are being found. Some humans however are even immune to the dominint type of fatal AIDS so it could be looked as like any other deasease (could never kill the whole specices as some people would live and become immune).
But what does this mean? It means that close relation between species allows for parasites and viruses to target those closely related species, easier. I'm not denying that mice and humans are closely related, but rats and humans are not.
It all depends on how it interacts with the organisim. Humans and mice might seem different, but we are also very simlar. We are both mammals, meaning we have a lot of shared mechanics which are universally targetable.
The most common example is selmonela, a strain of bacteria. Selmonela is a mutation of a strain of primitive gut bacteria found in a many kinds of animals. For animals that are reptiles or birds it is completly harmless and infact can even aid their digestion productivly (its just another type of gut bacteria for them). The problem is that Selmonela is now very dominent in farming produce and even some pets (it is a mutation that has become mainsteam).
If most mamals consume food with a small dosage of selmonela bacteria on it (including humans) they will not be very well (this is an understatement, humans die to this even with immediate and extreem medical attention). This is because mamals evolved to use a completly different type of gut bacteria to their reptile ancestors. Different as we are, a rat and a human both use the same type of bacteria (common ancestry although different individually). Selmonela does not like this bacteria much and because of its dominence in the gut it goes into a state of relasing toxins to try and flush it out. Most mamals can not tollerate this toxin and it causes extreem medical problems and in nature is almost always fatal. Normal lab rats infected with selmonela have a 100% chance of fatality to put it in perspecitve. Humans infected with selmonela are immediatly hospitalized and have a high chance of fatality (only thanks to modern medication).
An example of a similarity between us and rats.
Because some viruses, bacteria or fungus target specific metabolic processes, these metabolic processes can be generic or only altered slightly. Thus it is possible that a flu that only affects birds could jump to humans if the human exposes himself to huge doses of the flu viruses. Eventually 1 mutation could occur enabling it to affect the processes in a human.