The difference between the Bambino and the Sphynx is that the former has short legs due to dwarfism and the latter does not. Other than that they are very similar. In other words the Bambino is both a dwarf cat and a hairless cat while the Sphynx is a hairless cat of normal dimensions and appearance. The Bambino is a cat breeder creation. In 2005 Stephanie and Pat Osborne of the Holy Moly cattery crossbred a Munchkin and a Sphynx. The Munchkin is the founding dwarf cat. All dwarf cats have been created by hybridisation with a Munchkin i.e. they are hybrid cats: Munchkin x another breed.
The Sphynx originates in a discovered hairless cat in Toronto, Canada in 1966. The hairlessness is due to a spontaneous genetic mutation. For completeness, the Munchkin originates in a dwarf cat discovered by Sandra Hochenedel in 1983 in Rayville, Louisiana, USA, also a spontaneous genetic mutation. Both would not have survived but for being picked up by breeder and developed into cat breeds. Please click on the following links to read full details of these breeds. Thanks.
Some more on hairless cats