I am writing about two fairly rare cats here. I would expect that there are not that many people within the entire cat keeping population who keep either of these cat breeds. Of the two, the Sphynx is the better known. In fact you will find that the Don Sphynx is not mentioned in most of the books that you can buy in the West about cat breeds. If an author of a book about cat breeds writes about hairless cats, it is the Sphynx that is featured.
One reason for this is that the history of the Sphynx is part of the history of North America, while the Don Sphynx is Russian. Although there is a lively cat fancy in Russia, the largest cat fancy and largest domestic cat market place is North America. Therefore cats get discussed more in North America. Also more books about cats are written in English and therefore more widely circulated. Accordingly the Sphynx becomes better known. Although in Russia, a somewhat closed-off society still in 2012, no doubt the Don Sphynx is what people first think of when they think of a hairless cat.
Straight off, you probably would not see a difference between the Sphynx and Don Sphynx. I struggle to find real differences. My personal view is that a person thinking about adopting a hairless cat need not be overly concerned with the fine differences in appearance between these two cat breeds.
Referring to the breed standards tells us that they are very similar. The Cat Fanciers' Association (CFA), in the general section of their breed standard, says that this is a medium sized hairless cat that is warm to touch with a skin texture that is "soft peach or smooth nectarine". They say the cat is "sweet tempered and amenable to handling" and has "surprising weight for its size".
In America, TICA recognise the Don Sphynx (AKA "Donsky", another name for the breed) under preliminary new breeds . They have a breed standard. However, I'll refer to the general description of the breed standard of FIFe, which is a European cat association. The author says that, "The Don Sphynx is a solid cat, soft and warm to the touch. The specific feature is hairlessness".
As I said there is almost nothing to tell them apart in general. Note: the hairless coat of the Donsky takes four forms. "All but one results in hairlessness". So one version is not hairless. You will find that hairlessness in cats does vary. It is the same with the Rex cats which also have a mutation that affects the coat. However, I am sure your breeder will ensure that you cat is hairless as demanded in the breed standard.
As mentioned, the cats' history is the real difference but one that is not hugely relevant. The Don Sphynx is essentially Russian and the Sphynx North American. The history of the Sphynx is a bit confused so I want go over it in detail here. Suffice to say that the Sphynx is a selectively breed cat that started life as a mutated random bred cat discovered in Minnesota, America in 1975 and in Canada in 1966 and 1978 (source: Legacy of the Cat). The mutation that causes hairlessness in cats is not that unusual as can be seen. It just so happened that a breeder decided to create a cat breed from that mutation.
The Don Sphynx has a similar history but in a different part of the world; a mutated random bred cat was picked up by a breeder in Rostov-on-Don in Russia in 1987. Rostov-on-Don is in western Russia near Europe. In fact that part of Russia is considered European.
This is another major area of difference between these cat breeds. A recessive gene causes the hairlessness in the Sphynx while it is a dominant gene in the Donsky. That should make breeding easier for the Don Sphynx and there should be more hairless cats of Don Sphynx type roaming around Russia.
However, I don't think the genetic reasons for the hairlessness are of importance to people who wish to adopt a cat. The genetics of a cat (its "genotype") is the concern of cat breeders not cat caretakers.