Yes, there are several known breeds that have the curly, wild hair, the LaPerm, and the Devon Rex being two. Your top picture looks like a 'Munchkin" too with its short legs. These cats are missing an elemental gene in their coat makeup. thanks so much for sharing!
Its cross between the LaPerm and the Munchkin.
Curled up they look like a fluffy cushion..lol
I was actually looking at the Toygers but got distracted.