Why are some universal entities round and others are flat? I've been wondering for a while now why some objects in the universe (such as stars, planets, etc.) are round, while others are flat (galaxies, planetary rings and protoplanetary disks).

I know these shapes come to be because of gravity. In planets, the gravity from the core pulls everything to the centre, thus, rounding the planet (same with stars). But with Saturn, for example, why have its rings formed as rings and not as a spherical layer of ice surrounding the planet?

The same with the Kuiper belt and asteroid belt, I would presume the mechanics there are the same as with a planetary orbit, hence, why they are belts and not clouds. But then what about the oort cloud? Why is that a huge cloud in the outermost solar system and not a huge ring of ice.

As for the solar system itself, I've read that the solar system is kind of egg-shaped, but shouldn't it be just like the galaxy (or the other way round)?

I've tried looking into this and wondering about what different laws of physics may apply in each case, but it's all really confusing.
Preliminary note: there is a continuity of more or less flattened shapes. No macroscopic objects are really spherical, or really flat. Take Jupiter: it has a rotation period around its axis of 10 hours, and you can clearly see that it is an ellipsoid. It's the centrifugal force, combined with the gravitational attraction, that shapes these objects.

Now to your question: Planets and stars are dense bodies, and rotate as single objects. On the other hand, the Oort cloud, Saturns rings, stellar clusters and galaxies are made of independent particles, free-floating in lots of empty space. Depending on the formation history and gravitational environment (e.g., Saturn and its moons) of these entities, the orbits of these individual particles can be more or less co-aligned, and form a more or less spherical clouds.