The main difference is that they melt the cheese right off the wheel and they usually pair it with "grenaille" potatoes (basically a variety that's really small, so they are kind of roasted when cooked)

You can try it at home but you need specialized equipment to melt cheese wheel chunks, over here you can loan them from some cheese shops, it looks like this:

When eating it in a restaurant they will usually do that in the kitchen and just bring the partly melted chunk at the table and scrape the melted cheese into your platter though.
To be honest I'm not sure that melting the cheese directly from the wheel changes the taste, as long as you've got good cheese, but it looks glorious, and looks are actually a big part of the culinary experience so I think it still plays a part.

Also there's kind of a dispute over whether that process actually comes from Switzerland or not IIRC, but it is more widespread there nowadays