Dilute tortoiseshell describes a coat, not a breed. Where a standard tortie mixes black and orange, a dilute tortie shows blue-gray and cream, in patches or a fine marbled blend. The pastel shades come from a recessive gene a cat has to inherit from both parents, and the patchwork depends on two X chromosomes, which is why nearly all dilute torties are female.
Most are domestic shorthairs or longhairs, though the coloring also turns up in Persians, British Shorthairs and Maine Coons. Coat color says nothing reliable about personality, despite the folklore of tortitude. Dilute torties can be shy, outgoing, cuddly or aloof, so spending time with a cat tells you far more than the color does. In SF, that matters most for apartment living: look for a cat whose energy and comfort with noise match your building.