Yes, there are actually thousands of different types of Salmonella. The classification (taxonomy) of Salmonella is based mainly on so-called serotypes and phage-types. The first is a classification based on immunological characteristics, the second on susceptibility towards bacteriophages (viruses that attack bacteria).
The genus Salmonella is divided into serotypes, such as Salmonella typhimurium or Salmonella enteritidis. The serotypes can be further classified by means of phagetyping . These phagetypes can have a number, e.g. Salmonella typhimurium DT 140. Serotypes often have a name e.g. Salmonella London or Salmonella Madrid, reflecting the name of the city where the Salmonella was first isolated.
The same serotype may be present all over the world, each individual isolate is named a strain. You can thus have a Salmonella Madrid isolated from a patient in Madrid, but also from one in Cape Town. Both are the same serotype, but the isolates are 2 different strains.
More important than the name or phagetype is the behaviour of the different strains. Salmonella typhi is the causative agent of typhoid fever, a serious generalised infection. Most other types cause gastro-enteritis (diarrhoea) with different grades of severity. Some strains are particularly adapted to certain animal species, but can cause also serious illness in human beings, such as Salmonella enteritidis a type particularly prevalent in poultry and eggs.