They are very different. To belittle is to make someone feel small or insignificant, it is an action that is cruel on purpose. To underestimate simply means to not accurately guess the importance or power or value of a person or a thing. For example, you could say "I underestimated him as a tennis player." or "She underestimated how much food we needed to prepare for the party." "Disdain" is a feeling that someone is not worthy of your respect. For example, "He expressed feeling of disdain for liars and cheaters."