Bingo. We have owned several Manx cats over the years. They not only have bobbed tails, but they are unusually muscular cats; far more muscular than any domestic cat I have seen.
They come in "rumpies" and "stumpies". The rumpies will no tail at all, and the stumpies will have a very short stump of a tail. The bobtail feature is a genetic defect causing a shortening of the number of spinal vertabrae. Inbreeding will result in kittens born paralyzed due to too much shortening of the spine.