For example, let us take amorphous and crystalline quartz. While in crystalline quartz all bond angles are uniform, in amorphous form bond angles vary even though quartz has the same valency. Why is it so?
As a primer:
A requirement to qualify as crystalline, you need predictive patterns both in short, as well as in long distance range. In other words, there is a smallest structural pattern (unit cell) describing all atom's relative position well enough, which then is only replicated by translation. Which is the case in crystalline state (e.g., quartz, or sodium chloride), but not in the amorphous state (like glasses in general, not only quartz glass or glass in the windows).
However, it seems good to add some grains of salt:
- The property "crystalline" is about order. It is not restricted to "solid state". A solid sample may be crystalline, but needn't be -- glasses are an example. On the other hand, a crystalline material needn't to be solid -- think about examples of liquid crystals seen in LCDs.
- Mentioned "translation" may occur in all three directions in space. But putting an other unit cell just next to an other unit cell to build a crystal need not to occur this way, there equally are 2D (think about tiles in your bathroom) and 1D crystals, too.
- There are cases outside this strict discern "crystalline or armorphous". There are polymers neither fitting into one, or the other category with quite some impact on the physical porperties (cf. for example this reference). An other exception to the simplification above are quasicrystals, which are ordered yet not periodic; and still crystalline.
The variation in bond angles is much less than in the OP's diagram. Here is a bilayer of quartz observed under a scanning microscope:
It shows a transition from crystalline (left) to amorphous (right). In the transition, the number of rings with six silicon atoms decreases in favor of some with seven or five, mostly.
The amorphous form has higher potential energy (some bond angle strain) and I guess higher entropy. Glasses are metastable, meaning that the crystalline form is thermodynamically favored, but the kinetics of reaching it are very slow.