Comet Halley
Long and short period comets

Comets coming from the Oort cloud and the Kuiper belt have very different properties and behave differently. First of all, these two classes of objects have distinct dynamical properties, being gravitationally affected by different objects. Second thing, comets coming from the Oort cloud and the Kuiper belt have respectively long and short periods, with different orbital characteristics. Furthermore, having been formed in different places, these two classes of objects don't show a similar overall chemical composition.

Dynamical properties

Comets coming from the Oort cloud and the Kuiper belt present dynamical differences since they are affected by different bodies. In fact, inhabitants of the Oort shell are only loosely bound to the Sun and so, they are easily disturbed by events that might occur beyond the solar system. If the Sun passes by another star (or a massive molecular cloud) some of these comets are jarred, and can be swung into an elliptical orbit that can bring them toward the solar system. On the contrary, comets belonging to the Kuiper belt cannot be directly disturbed by stars other than the Sun. For these objects, the planet Neptune, whose orbit lies very near to the belt, plays an important role in stabilizing their orbits or, on the contrary, in throwing them away from their previous trajectories.

Short and long period comets
A second important difference between comets coming from the Kuiper Belt and from the Oort cloud is represented by their different characteristic periods.
In fact, short period comets are thought to generate in the Kuiper belt and have rather predictable orbits with short periods (up to 200 years). There are two major families of short period comets: the Jupiter family with periods of less than 20 years and the Halley family with periods form 20 to 200 years.
Even if their orbits can be predicted with some accuracy, some of these short period comets might be gravitationally perturbed and become long period objects. In fact, gravitational effects of the outer planets can cause these bodies to alter their paths into highly elliptical orbits that take them close to the Sun. Such events are unpredictable and, to make predictions even harder, in extreme cases comet nuclei can break up (as in the case of the famous comet Shoemaker Levy 9)
Long period comets, on the other hand, are thought to generate in the Oort cloud and have unpredictable orbits, randomly oriented on the celestial sphere, with periods much longer than 200 years. They can return on their steps after periods of thousands to millions of years (or not at all) and so they are difficult to detect and catalogue.
To cause such bodies to leave the Oort cloud and approach the Sun, some mechanisms are needed such as the relative movements of nearby stars or massive dust clouds or the shock wave from an explosive event such as a supernova. Whatever the mechanism, only five to ten significant cometary bodies of this kind approach the Sun each year, while an unknown number of smaller bodies pass undetected.

Different compositions of long and short period comets

The chemical composition of long period and short period comets is similar, although the first ones tend to contain more volatile. This can be explained by the fact that short period comets outgas huge quantities of volatile at each approach to the Sun while long period comets visit the inner solar system only rarely, retaining much of their icy material and mass.
Another chemical difference in the composition of long and short period comets can be introduced by the fact that Oort Cloud objects are thought to have formed closer to the Sun than the Kuiper Belt objects. In fact, during the formation of the solar system, small objects formed first in the inner part of the disk, near the giant planets. These objects would have then been ejected from the solar system by gravitational encounters, and those of them that didn't totally escape could have formed the distant Oort Cloud. The small objects that formed farther out, were born later on and having no such gravitational interactions with the planets, remained as the Kuiper Belt objects.