The difference between Egg Pasta and regular pasta is all in the yolks.
Yes there is egg in regular pasta. I use it in my homemade pasta recipe and most Italians that I know use egg in there recipe too.
However, if you're making or using an egg noodle you are only using the yolks. Although I've had some really tasty noodles with milk and butter in the recipe as well...
Why only the yolks?
The yolks give the pasta a softer texture and richer flavor. This type of pasta you wouldn't normally use in your Italian pasta recipes. This is something you'd want to serve with some nice, thick soups and stews, or a goulash or kugel recipe.
The shape of an egg pasta is more like a noodle. Cut short and wide with a wiggled shape and definitely not as thick as most pasta shapes.
There are a variety of Chinese egg noodles. Almost always served in a soup or chow mien. Round and long rather then the short sister shape you'd find in a kugel.