The difference between breeds and species? Well, think of it this way. There are many different breeds of dogs, from chihuahua to great dane, but they are all Canis familiaris, e.g. the domestic dog. There are five types of domesticated hamster, however, they are as different from each other as dogs and cats, or horses and snakes. The five species are:
- Mesocricetus auratus, the Syrian or Golden hamster
- Cricetulus griseus, the Chinese hamster
- Phodopus sungorus, the Winter White dwarf hamster
- Phodopus campbelli, the Campbell's dwarf hamster
- Phodopus roborovskii, the Roborovski dwarf hamster
One exception to this is that hybrids between the Winter White and the Campbell's are possible. However, this is not because they are different breeds of the same species. Rather, it is because the two species are similar enough to mean that mating the two hamsters can produce young. It is similar to how a horse and a donkey can breed to produce a mule, or lions and tigers can breed to produce ligers.
This hybridisation would not happen in the wild, however, and there are many potential risks involved with hybrids as opposed to their non-hybridised counterparts, so I would never recommend breeding them.