Forgive my ignorance here, but what is the fundamental difference between a gooseneck trailer and a fifth-wheel?

Is it just the way they hook up (I realize the gooseneck hitches to a ball in the bed of the towrig, and a 5'er slides into a receiver like on a semi), or is there more to it than that? Which is preferred and why?

I am no expert but I think you answered your own question. I think it simply how they hook up. I think people would prefer a gooseneck for one reason. That is when you have a standard fifth wheel hitch there is a little slop in it. So when you stop or take off the trailer will move a little forward and backward. It makes a little noise from what I have heard.

Fifth wheels are more stabile in crosswinds and goosenecks are better for traveling off road (like a hay field).

And, goosenecks are for the most part the economy method of distributing trailer ("tongue") weight between the steer and pull axles of the towrig. I've seen some higher dollar gooseneck setups with sliding plate, but most gooseneck balls are stationary and still require careful loading of the trailer loads to achieve best weight distribution.

On the other hand, most 5th wheel setups are sliding plate deals that provide a great deal of flexibility in shifting weight between the steer and pull axles, eliminating most of the care in trailer load placement. Either way affords getting maximum load capacity from a trailer without exceeding rear axle weight capacity of the towrig.