I've never known there was a 'koi' type, but I imagine the difference would be marbles can change they're entire appearance over the course of a few weeks. It's a genetic code that's passed through breeding. My Seiya is a marble, was a full teal on one side, camouflage teal/white on the other, now both sides are camouflaged white/teal and he's developing black on his belly, anal and pelvis fins. Marbles will change color throughout their lives.
'Koi'....I don't know anything about them. Perhaps it's another name for marble? Or maybe it's a multi-color with a specific pattern. Or maybe 'koi' just describes the pattern.
Sorry, don't know much about the latter, but I did lots of research on marbles after I got Seiya.