Awesome, I did some looking into it but never saw any discussion of hair length. I was reading about the lore of them and wanted to ask before getting any deeper
Likely your cat is a Tortoiseshell (colouration) Domestic Medium Hair (breed). Often people just refer to colouration and not to the breed, like how people call cats "Tabbys". Tabby is a colour pattern, not a breed. Most common breeds are Domestic Short Hair, Domestic Medium Hair and Domestic Long Hair. Of course there are many other breeds but most shelter cats are just Domestic X's.