Well. I've been reading a lot of manuals on Simodrive and Siemens Masterdrives recently. And for them, a single axis setup is just a drive that controls just that, a single axis of movement (Be it linear, rotational, or what ever your mind could imagine). A multi-axis setup is a system with more than one axis, either the same item moves multiple directions using different servos, or different items move using seperate servos. They also had single drives that could control more than one axis.
I'm no expert, just beginning in this field. But I think it's safe to say that it would be similar across all boards. An axis could be linear movement in X, Y, or Z, or a rotational movement (usually A or B). Multi-axis just means more than one plane of movement.