Harry Potter: Invisibility Cloak?? [SPOILER ALERT]?

Ron said that the cloaks are very rare. But in one of the books they said there were multiple kinds of invisibility cloaks. Harry's can't be summoned by spells, but others can. Some cloaks just have a charm put upon them but can be hit by spells. Another kind of cloak starts off invisible and will eventually fade to a color fabric. That's all I remember. I think Harry's was one of a kind, but there are other less extravagant cloaks.