By the looks of it, the red and orange pairs are the stepper motor wires. Even without the fact the board has 4th Axis Drive written on it, the pair of chips mounted to the heatsink are very much like an old stepper motor drive.
I'd also guess red are one pair, and orange the other pair.

As for the multicore wiring, I'd power things up, and see what kind of voltages you get on the wires, as that'll give us an idea of what they might potentially be.