Are you asking how they're different, as in what makes the different hairs come out the way they do?
Or, is it wondering what the point in the difference is?
The first one is pretty easy. Follicles. The follicles determine how hair is shaped, how it feels, and how thick it is. The way they chain the materials together determines how straight/curly it is, how coarse/smooth it is, the diameter, and how long it grows before falling out and getting replaced. You can look at cosmetology faqs for the details. There's some debate on some of the details, but that's the gist of it.
As for why there's a difference in anything but length, that's harder. Evolution is the broad answer. At some point, the genes that made our hair the ways it can be were advantageous enough to end up fairly universal for all humans.
There are no certain answers, and I don't think it's possible to have many when it comes to that side of things. But, the two big ideas I've read about or heard about are friction vs scent and display vs temperature.
When it comes to pubes, there are people that have the hypothesis that they're pheromonal concentration and dispersion assistance. There's also the idea that they prevent friction leading to skin injury over time, and/or during sex.
Between those two, I kinda doubt the first. Humans just don't have much in the way of pheromones, and we suck at detecting them. Seems pretty strange to need the coarse and curly hair down there when the associated senses aren't there. The second makes sense on the surface for sure; just shave your junk and put on some stiff pants and you can tell the difference with and without pubes in five minutes. And there is a degree of increased skin irritation without hair, but I don't see that as being as big a factor. I personally suspect air flow has a factor in there, but I have nothing to back that up with other than genitals being very temperature responsive and humidity needing. But I admit it could be both or neither, I sure don't have the expertise to say (and there aren't many people that do)
Head hair, you get the usual debate on it growing the way it does for environmental protection against heat and cold, usually versus the possibility of it being for display. I say it's both because it's pretty unusual to find any critters with a major trait like that not having multiple functions.
Anyway, years ago, I asked the same question and went digging. I didn't give enough of a fuck to write things down, but that's the basics I picked up.