The sun emits sunrays in every direction. But as the sun is very far, the sun rays that reach us are practically parallel. From Earth, any two sun rays form a maximum angle of ~0.53°. Sun rays are practically parallel, but not perfectly parallel.
For most practical purposes, we can assume sun rays are parallel for simplification. But in other cases, the small angle is critical to the problem & we need to take it into account.
With something like a sundial, we do not have to account for such a minuscule angle because the gnomon is not far from the base and will not affect the function of the sundial.
On the other hand, in the case of eclipses, the objects involved are much larger and much farther. Therefore, the angle of sun rays is critical to the problem, and we have to consider it. We need the angle to determine the type of solar eclipse (total or annular), the path of totality, the length of a total lunar eclipse, etc.