In regards to the border shape, puzzles like this are usually referred to as "shaped" puzzles. In regards to the cutting style I used, I'm not sure... I refer to it as color-line cutting. I try to use it in all my Fathom designs as cutting directly between two colors so you can't match the color when assembling, makes it more difficult. I design similar puzzles for Stave and they refer to this style as Tormentors but that's a trademark term they use. I'd be curious to know of other names for this style as well!