She's lovely! I would describe her as a brown patched tabby domestic shorthair. You can also refer to her color as torbie (tortie tabby). Her tabby pattern is somewhere between mackerel and ticked; it's not uncommon to see random-bred domestic cats with a lot of ticking that obscures the mackerel tabby pattern. The red/cream tortie patches also tend to obscure the tabby pattern.
Short tails can be caused by many different things. Several different mutations are known to cause short, bobbed or kinked tails, and there are no doubt many other mutations out there in domestic cat populations that haven't been studied. Short tails can also be caused by injury to the tail. I had a cat many years ago with a tail about the same length as your girl's tail, whose mother had bit off the end of his tail just after he was born; we thought maybe she was confused between his tail and umbilical cord.
Most cats are not any particular breed, but that doesn't make them any less special... your girl is gorgeous and has her own wonderful, unique combination of traits!
I have a full torture with no tail (born that way,) but she is half manx. I sort of wondered if my Yoonji was too, since they share a few similarities.
This doesn't look like an injury to the tail to me. It looks genetically stubby because it's also way thicker than normal. I actually see what *might* be a little Japanese Bobtail in the face, but they normally have kinked tails, not merely stub tails that aren't kinked.
In fact I can't really identify this tail. It's cool though. I like it.
This cat has a lot shorter fur than that grey one. Just IMO the tail base probably shouldn't be quite that thick. Also in yours there's slight evidence of unevenness.
Actually you know what? I take that back. I would want to feel the tails in question before I say this.