is there much difference between the two
In my experience, "Swiss" is the name given in the States to almost any cheese with holes in it, remotely (or not so remotely) close to Emmental (the Swiss make many more styles than Emmental - think, Gruyère, Berner Alpkäse, Appenzeller, etc., and hundreds of others - so "Swiss cheese" is usually a blanket misstatement).
Though technically "Emmental" has AOC protected-status in Switzerland, there are variants (under similar title) in France and, as I just found out, Germany. These cheeses have pronounced eyes from propionibacterium lactic-acid fermentation; a typically pretty mild, nutty taste; and a medium-firm texture. They can become more aromatic and piquant, with longer aging.