What is the difference between a network hard drive and a home server?

I see that a server is basically a type of computer while a network hard drive is a hard drive accessible over the internet, but is there any main difference or which one is more useful for home media?What is the difference between a network hard drive and a home server?
Either one is ok for home media. A server is designed to run other things, like databases, web servers, etc. A network drive is dedicated to being just that, so in theory, it should be faster....