"Uni" usually refers to the sail plan. When the boat is referred to as a "uni-rig," it means mainsail only.

Lots of boats, with two or even three sails can be sailed "solo," meaning by one person, even though the boats are not uni-rigs.

And, of course, a uni-rig can be sailed with more than one person on board, but the boat itself is still a uni.

Now there are uni-rigs that also have spinnakers, so I don't know whether they are still technically uni-rigs or what you call them. They are one sail upwind and two sails downwind. Anybody know whether this is still technically a uni-rig? I would think not.