I do not know when the term “haredi” came to describe those in Israel – and in various parts of the Diaspora – who are most scrupulous about their Jewish observance, and demand that other Jews observe the same way. There is the hubris connected with the term that suggests that if anyone observes Judaism in ways different from a haredi person, they are less Jewish, or not Jewish at all.
If I would estimate, by my various visits to Israel, when this term came into use, I would guess that this term grew into common usage among the Israeli population after the Six Day War, when religious Zionists were seized by a great enthusiasm for settling in and holding onto occupied territories. It is often a derogatory term when used, obviously, outside of the Orthodox community.
As background: The word “haredi” comes from the Hebrew bible; Brown-Driver-Briggs’ “Hebrew and English Lexicon of the Old Testament” defines the verb “h-r-d” as “trembling,” “being terrified,” or “being startled.” It somehow morphed to mean ‘ultra Orthodox,’ or ‘ultra observant.’ In this respect, it is quite close to the Hebrew root “y-r-a,” or “fear/revere.”
I disagree with the premise of your question, that there is difference between a “fanatic” and “more moderate Haredim.” I think the phrase ‘moderate haredi’ is an oxymoron; that is, someone who is called haredi, or uses that term about himself, is already far beyond the border of ‘moderate,’ and has gone to fanatic. I would say that, at least in English, the word “ultra Orthodox” is different from haredi. “Ultra Orthodox” implies a state of person observance; “haredi” implies someone who has not only adopted a strict Orthodox life for himself, but has gone to the extreme of cutting off from his life any non-Orthodox person or practice. In other words, ‘haredi’ is the most extreme of individual, advocating for nothing less from his life.
To sum up, I think the terms “haredi” and “ultra Orthodox” can be used to describe different levels of religious zeal, the former nationalistic and exclusivist, the latter personal and not being pushed upon others.