This is an interesting discussion, and I think that the various answers and opinions reflect a range of underlying assumptions. I'm not sure it's really of much practical importance, although it is one of those things where a misunderstanding could lead to erroneous conclusions that result in technical errors for those who try to "make it happen."
Is a turn "round" (part of a true circle) or simply curvy and "rounded"? Could be either, right? A good skier can ski a line of pretty much any shape, with the right blend of skills. But in reality, I think that very few of our "round" turns are actually, technically, round.
Whatever the shape of the arc, do the arcs of both skis share the same focus ("center")? Sure, sometimes. Surely not, at other times. Should they? I'm not sure why they should.
Are the tracks of the front wheels of a car "parallel"? Parallel curves are defined to be the same distance apart at all points. But that depends on how you measure it, doesn't it? Obviously, the car wheels' mounting points on the chassis don't change, and the car's width does not change, so the length of a line between their pivot points remains constant. (Some sophisticated suspension and steering systems, tire flex analyses, and such may possibly alter this simple relationship slightly. I don't know, but for simplicity, let's consider that the wheels steer on simple pivot points, each about a fixed axis, at each end of a fixed-length axle.)
So the wheels remain the same distance apart at all times. But what about the tracks? It depends upon which points on each track you're measuring from, doesn't it? Let's imagine an abandoned highway heading due north, where we "slalom" left and right across the freshly-painted (so we leave tracks!) centerline, weaving a tight sine-wave-shaped path. Do the tracks remain the same distance apart? It depends on whether we measure them along a line perpendicular to one track or the other, or along an east-west line (perpendicular to the center line). I know--this analogy cries out for an illustration, but anyone with a good imagination should be able to picture what I'm describing.
Perhaps a simpler way to look at it arises from looking once again at the exercise known as "pivot slips." Here are a couple familiar animations that I have posted before (copyrighted):
(Please excuse the Neil Diamond reference. It's a long story...based on the torture that some people find this maneuver to entail!)
Skier's feet (stance width) remain the same distance apart throughout, but skis appear to move closer and farther apart.
In these animations, the feet (the skis' pivot points) remain the same distance apart from left to right. Yet the skis appear to move closer and farther apart--just like the wheels and tracks of the slaloming car. (In theoretically "perfect" pivot slips, the skis would actually move on top of each other when they rotate 90 degrees across the fall line. In reality, the skier's pelvis must pivot at least a little to allow the skis room, as shown in the overhead animation.) If these skiers were to engage their edges appropriately to make the skis travel the direction they're pointed, these pivot slips would become turns--but the relationships of the feet and skis could remain the same. Measured from left-to-right (perpendicular to the fall line), the tracks would remain constantly the same distance apart. Measured in a line perpendicular to the skis, the track width would vary--narrowest in the transition, and widest at the apex (the fall line, in this case).
Does it really matter? For most skiers, these picayune dissections of technicalities probably don't matter at all. I doubt that understanding it is necessary for anyone, just to make great turns. But misunderstanding concepts like this often create a very wrong image of what "should" happen in a skier's mind, and that image can translate to quite wrong movements! I've seen instructors attempt pivot slips with the mistaken mental image that their skis should remain separated the same distance throughout. That mistaken notion causes them to rotate their pelvis and upper body, rather than their legs in their hip sockets. In an exam, that's a fail! And when translated into actual skiing, it's a critical handicap.