Pancit (pansit) is a catchall term for Chinese-influenced noodle dishes in the Philippines. There are many different kinds of pancit — different noodles, different ingredients, different styles of cooking. Here is one recipe for pancit using egg noodles.
Bihon refers to a type of pancit (Chinese-influenced Filipino noodles). These are thin noodles made from rice flour. Bought dry, they look like very thin white sticks, so they are also known to English speakers as rice sticks.