'Sausage' dogs are Dachshunds. They come in two sizes, one is just called Dachshunds (although they are often wrongly referred to as Standard Dachshunds) and the other is called Miniature Dachshunds. Miniatures must ideally weigh no more than 11 pounds in the showring. They come in three coat types, Smoothhaired, Longhaired and Wirehaired, so there are six varieties altogether.
They were originally bred to hunt badgers, which is why they have short legs with turned out front legs, to turf the earth out of the way when digging into a badger set.
There are many varieties of miniature pigs, Vietnamese Pot Bellied Pigs are not as big as some 'farmyard' varieties and are often kept as pets, and there is a breed called a Kuni Kuni.