Yes, domestic short or long hair is just a catch all term for non pedigree cat.

For coloring your cat is a TorBie.

quoted from website below. "Torbie is short for tortoiseshell-tabby. When you add tabby stripes a tortie becomes a torbie."

See this website for the names of different color patterns on cats. It has lots of great photographs as well.

What color is my cat?