Just to clarify, the metal in 99% of HI khuks goes from the tip of the blade to the tip of the handle. The little silver spot you see in the back of the handle is the tang, peened over the brass butt cap to help hold everything together.
The "chiruwa" style blades have an exposed tang and slab handles. This is the same construction you see with may popular "combat" knives - such as Busse, newer Chris Reeve, Strider, etc. Every knife from HI that has the two (or three) handle rivets has this style of tang, to my knowledge. This is definitely a solid handle style, and somewhat easier to modify if you want to put a new handle on. There may be small gaps between the metal and handle material, due to shrinkage of the horn or wood scales.
The second common style is the "hidden", "rat-tail", or "through" tang. In this style, the handle is one piece. A hole is bored all of the way through the handle. A piece of metal extends from the back of the blade, all of the way through the handle, and comes out the end of the brass butt cap. This tang is not as wide as the chiruwa style, but is thicker and would be quite difficult to break. I believe Randall knives are built this way in many styles. The through-tang construction gives a seamless handle, and many people say this style transmits less shock to the hand during heavy chopping. This style is also more common on antique khuks.
The stick tang has gotten a bad reputation from bad construction techniques that are not used in HI blades. In these cases, the tang does not go all of the way through the handle. In inferior khuks, the tang may go only a few inches into the handle, and is glued in place. Often, there will be a nail in the center of the butt cap to mimic the proper tang exit point, and to hold on the butt cap. This is easier to do, and may be worth it if the kami lives in your village and you can go yell at him when your knife falls apart. Not so good for the export market, though. The second form of inferior construction involves some sort of screw extension. The tang is threaded, and goes part way into the handle. Sometimes that's it, and sometimes there is a bolt coming from the butt which screws into the tang. This type of construction was popular in military contract knives and similar stuff in the '80s. Often, the parts that screwed together were pretty thin, and either unscrewed or broke under hard use. Again, HI does NOT use either method.
The third style of HI handle is pretty rare. This is a partial tang with a single pin. Like the through-tang, the handle is one piece. However, the tang only extends a few inches into the handle. As discussed above, this is potentially weak, so a rivet is placed through the handle and tang to give extra strength. This style is used on handles with extreme bends or curves where boring a straight hole would be very difficult. This style looks similar to the chiruwa handle, but only has one rivet near the blade-end of the handle. Uncle Bill suggested that end users could add a similar rivet to partial tang models that HI occasionally acquires from non-Bir Gorkha kamis.