What is the difference between a planet, a moon, a dwarf planet, an asteroid, a comet, etc? I'm interested here in objective, unambiguous differences. Arbitrary distinctions such as the actual mass or dimensions of the object are at best a last resort.
All of these things are satellites, orbiting a star. A few definitions are easy to pick off:
A comet is an object with an orbit so eccentric that the heat and solar wind from the star cause large amounts of detritus to be driven into space every time it approaches the star. Thus it is possible for a comet to change its status over time: once enough stuff has been blown off, it becomes an asteroid.
An asteroid is an object which is no longer getting stuff blown off by the star (everything starts out that way) but is small enough that gravity does not deform its shape into a spheroid.
A planet is an object which is large enough that its own gravity has turned it into a rough sphere, and is in orbit around the star itself. A distinction is made between Planets and Dwarf Planets, in that Dwarfs have not cleared their orbit, where full Planets have. Factors that affect this include size, distance and eccentricity of the orbit, and distance to the star. A quite large planet on a very long orbit might not have cleared its space, while a small planet on an eccentric orbit might have.
A moon is a satellite which is orbiting a planet. It might be asteroid size or dwarf planet size. There's an interesting theoretical case where a pair of planets is orbiting each other and the star. There are none of these around our star but it's a case which deserves analysis. My thinking is that if the Center of Gravity of the combined pair is inside one of the objects, then they are planet and moon. However, if the second object is large enough and the orbit circular enough that the CG is in the space between, they are both planets. co-planets maybe?
The way a solar system forms is that it starts with a mass of tiny particles, chaotically distributed. They might be individual atoms or molecules, in which case we call it a gas cloud, or it might be larger chunks. There was some initial event that caused all of these particles to be in one place--perhaps a different star blew up, or maybe something else. But at the start of the analysis, they are near each other (within a few light-hours?) and moving in random directions, and there are enough of them that all of the particles are in orbit around all of the others.
Now and then, there are collisions. If the velocities are different enough, and the collisions are inelastic, the particles lose a lot of momentum, and they fall to a lower orbit. This quickly causes a clumping of these lower velocity particles, which will tend to be in the center. When the collisions are elastic, the particles bounce off in a new, highly random direction, but when they are inelastic, and the velocities are similar enough, they'll stick together and form larger and larger clumps. Most of the particles lose enough velocity through this process that they fall into the center, but a few wind up in an orbit around the central mass. Based on observations, it appears that nearly half the time, the center is actually several objects, which eventually get big enough they form double or triple stars. Among the inner orbits, anything that's very far from circular quickly collides with something else, and the new mass adds their vectors to make a new orbit. If the velocities are different enough, they fall into a lower orbit, or the star. Large planets tend to attract lots of stuff and grow ever larger, and they also cause perturbations in the orbits of smalller objects, leading, eventually, to collisions.
Anything with an orbit that is out of the plane with the others will eventually have one of these velocity-sapping orbits, so eventually all that's left are things that are mostly in the same plane, or a few things that have managed to miss hitting something bigger to survive for a long time. The direction is determined by the small statistical differences from the initial conditions.
There inevitably be some clouds that have too little mass to create a star--these turn into brown dwarf stars or sometimes rogue planets. There are probably a lot of them out there, but since they do not emit light, they have to block or otherwise interact with something for us to detect them. A lot of it is simply interstellar dust. It may turn into something if it collides with other objects or dust clouds, but for now, it's just dust.
