I got the cats' DNA results back! Interesting stuff! I'm not as familiar with cat breeds as I am with dog breeds...
I thought Toasty would be more Siamese, and didn't expect these big long-haired breeds, or the Scottish Fold, but these things happen!
Didn't expect Graham's bits either. I had never heard of the Highlander, so I had to look it up. It's a new breed, bred from the desert lynx and the jungle curl (two other newer, rarer breeds). Graham doesn't have the curled ears they generally have, but he's got the large build, bob tail, tabby pattern, and friendly dog-like personality.
...Out of interest, the desert lynx has no wild cats in its background (other than rumors of possible bobcat way back), but the jungle curl is a cross between the American curl and the African jungle cat.
In the end they are both mostly American domestic cats and it's not that important either way, but it's so cool to find this kind of thing out. I'll keep calling them a Siamese and a bobtail in casual conversation.