The word vermicelli translates literally to "little worms". This pasta is very thin rods, like spaghetti but thinner. Vermicelli can be used broken up in soups, or used as a pasta with a sauce or even as noodles with Asian ingredients. A well-known Mexican dish that uses this pasta is Sopa Seca de Fideo.
Find this pasta in most any well stocked grocery store.
Rice vermicelli is a thin noodle made from rice flour and water. These noodles are used in Asian cooking. These thin noodles don't require cooking you can simply add them to a pot of boiling water, turn the heat off and soak the noodles for about 5 minutes until they are tender. Alternately, they can be soaked in cold water for about 25 minutes until tender. If you're going to use the noodles in a stir-fry, don't over soften them or they'll get mushy.
The softened noodles are commonly used in Vietnamese Salad Rolls (fresh rolls).
These noodles are easy to find in most any Asian grocery store and even in well-stocked large stores like Walmart. Of course you can find them online at Amazon.com Rice Vermicelli.
Here are some substitutes for the Italian pasta as well as vermicelli used in Asian dishes:
Wheat pasta ingredients: Semolina flour, salt, water
Rice vermicelli ingredients: Rice, Water, and Tapioca starch
Remember actual ingredients may vary by brand.