Why is that? There are some objects in the gap, but why are most of the Oort cloud objects in one area? Shouldn't it also fill the large gap in the picture just as much?
There is no "gap" other than an apparent one caused by the use of logarithmic axes.
The density of Oort cloud objects is thought to decrease with increasing distance from the Sun. However, the volume of a shell in the base 10 logarithm of radius increases by roughly 1000 for every order of magnitude increase in radius.
That means although there is a higher density of objects at smaller radii, they are fewer in absolute number. i.e. There are roughly 1000 times more objects between 10000 au and 100000 au than between 100 au and 1000 au, but with about one thousandth the volume density.
However, there is a dearth of asteroidal bodies between 100 au and 10000 au with high inclinations. i.e. The objects that are there are still confined to a broad disc. That is because most of the Oort cloud objects are ejected from a disc in the inner Solar System and then only the outer objects have their inclinations randomised by the tidal field of the Galaxy. See What's the reason for the hollow region in Oort cloud? .
The Kuiper belt and the Scattered disk are widely believed to lie in the space between the outer planets and the Oort cloud, but not to reach all the way out to the Oort cloud (apparently due to resonances with Neptune and a scarcity of sighted object much outside the 1:2 resonance orbit). The various dwarf planets of the outer solar system are sometimes referred to as Kuiper belt objects.
As I understand it the Kuiper belt is expected to be distinct from the Oort cloud in being at least somewhat planar and aligned with the ecliptic whereas the Oort cloud is essentially spherical. If Pluto can be taken as a guide then we expect considerably larger inclinations from Kuiper belt objects than we see from large bodies in the inner solar system, but still a nod toward the ecliptic.
I've less familiarity with the scattered disc and the Wikipedia articles indicate that the usage is not very consistent. It seems to mean highly eccentric objects beyond the orbit of Neptune.