The difference is that they're two different species of animal! The closest analogy I can think of is like a dog and a wolf. Genetically different enough to be a different species, but close enough to hybridize. WW's have few colors, with theirs being less patterned and overall just less complex. Campbells have many more colors from opal, to argente, to mottled. This highlights just a few of the differences.
Campbells- live in the desert areas of Asia and China
WW- live in Siberia and Mongolian desert areas
*Note the difference in place of origin*
Now for taxonomy and classification
The Campbells-
"Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Rodentia
Family: Cricetidae
Subfamily: Cricetinae
Genus: Phodopus
Species: P. campbelli
Binomial name
Phodopus campbelli
(Thomas, 1905)"
The winter white-
"Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Rodentia
Family: Cricetidae
Genus: Phodopus
Species: P. sungorus
Binomial name
Phodopus sungorus
(Pallas, 1773)"
"Russian dwarfs" aren't technically a species, but rather a mix of two. It's a real shame as it causes the death of pure blooded WW's and Campbells, along with with a myriad of health problems. If you want more info, here's a good rundown of what's happening
Hybrid Dwarfs - Harvey Hams
Google of course could help some
Hope I could help a bit!