This summer, a horde of astronomers decided what the word “planet” means. Their definition is a sensible one; essentially for an object to be an officially-sanctioned, bona-fide, regulation Planet™, it must:
...I made that last one up.
Furthermore, the same gaggle of telescope-botherers decided that a “Dwarf Planet” is anything that:
So the only difference between a “Planet” and a “Dwarf Planet” is the requirement of having “cleared the neighbourhood”. This means that a Planet is overwhelmingly massive and has an overwhelming gravitational influence on nearby objects. And therefore all the objects with which it shares a similar orbit will have either: been flung away; assumed an orbit that is governed by the planet (such as going into orbit around it); or just crashed straight into it and thereby ceased to exist. A Planet clearly dominates the vicinity of its orbital path.
By the way, the last Dwarf Planet criterion up there was another comedy fabrication. You guessed that, right?
This means that the difference between a Planet and a Dwarf Planet is not just its size. If you stick a fairly small chunk of rock in an orbit on its own, with only a few measly specks of dust for company, it'll easily bully them into submission. But put the same chunk of rock in the ring with something much bigger than it, and it'll become the larger object's biatch without hesitation.
So the Dwarfiness or otherwise of a Planet-like object depends on whether or not it's surrounded by similarly heavy objects, rather than any intrinsic property of the thing itself, for example its size. And so “dwarf” is a bit misleading.
Note also that a Dwarf Planet is not a Planet. The name makes it sound like a sub-category of “Planet”, but it's not. Similarly, a minor planet (an asteroid or similar) is not a Planet under the IAU/UAI's definition of what constitutes a Planet.
And that's very confusing.
Even before the “re”definition, people had been calling asteroids “minor planets”. That name comes loaded with the implication that the other things known as “planets” were, more specifically, “major planets”. Whenever anyone used the word “planet” without qualification to mean only major planets it was because: they didn't know that minor planets existed; there was sufficient context to make the adjective unnecessary (such as comparing planets to stars or “asteroids”); or they were just being lazy. (Y'know, like on the several occasions when I've said that Pluto isn't a planet.)
So I reckon the use of the word “planet” in place of “major planet” has always just been shorthand – the unqualified term has always been used loosely. This is why I think that while the definition the IAU came up with was good, it should have been defining the term “major planet” (or perhaps “classical planet”) rather than just “planet”.
Let's consider the situation a bit more sensibly.
Mars is a giant rock. Yes, it's got some water and various other chemical substances lurking in and around it, but that just makes it a wet rock. An asteroid is just a smaller chunk of rock with a fair amount of ice chucked in for good measure. A comet is just a particularly icy chunk of rock that exhibits a tail as this ice evaporates. Earth is just another wet rock, with some animals and plants on it. If you chuck your drink on a mossy rock and then stand on it, that is then also a wet rock with an animal and some plants on it. A pebble is a smaller rock, possibly with a few animals or plants nearby.
The only differences between any of these are their size, their shape and the details of their composition. (Note that in planetology, “ice” needn't be water – it means any simple chemical compound, usually but not necessarily a solid. For example, Uranus and Neptune contain water ice, ammonia ice and methane ice in various proportions.) So what's a sensible way to categorise them?
The universe is generally homogeneous – everything is made of the same stuff. Some clever people pointed telescopes at the most distant galaxies they could find and spectroscopically analysed the hell out of them, and it turned out that they were made up of much the same stuff as our galaxy. That's how we know. There's no enlightenment to be had by categorising things based on their composition, because everything's pretty much the same anyway.
Size is also a dodgy naming criterion because sizes are usually continuously distributed. You'd have to pick a number and say that anything slightly bigger than that number is a widget, and anything slightly smaller is a fudget. Then if it turns out you measured its size wrongly, your widget becomes a fudget.
Picking an object up and dumping it somewhere else doesn't change what the object actually is. That's pretty obvious. (Well, unless you stick some bread in a toaster, but then it's the heat that's causing it to change, not the movement; anyhow, the protons, neutrons and electrons are all still the same, just rearranged.) So a body orbiting a planet wouldn't become something else if it suddenly started orbiting the Sun.
It's not even sensible to use an object's shape as a naming criterion. It's impossible to quantify by how much an irregularly shaped blob differs from some pre-defined shape. Even if it was possible, you'd still have to pick a boundary and we'd be back to the widget/fudget scenario.
So let's just call anything in space that's important enough to be identified individually a “planet”.
...Unless there's nuclear fusion going on inside it and it's therefore a star.
I don't care whether it's successfully bullied everything out of its way, or if it's been the victim of the bullying; nor whether it goes 'round the Sun in a near-circular orbit in the plane of the ecliptic, or if its orbit's the shape of Bert's head and it's flying 'round the Sun at a funky angle; I don't care if it's the shape of Bert's head; I don't even care if it's going 'round another planet instead of the Sun. It still the same thing – it's still a planet.
This is actually what most people mean when they say “planet”, and that's why minor planets and Dwarf Planets have the word “planet” in their title, and why the constituent particles of Saturn's rings aren't called planets.
That's not to say that all planets are equally important, though, and it's wrong to suggest that a planet like Earth or even Saturn is equivalent to Jupiter in magnitude. Jupiter's barycentre with the Sun lies above the Sun's visible-light surface; this is one of the proposed criteria for distinguishing binary planets from primary-and-satellite pairs of planets – it's that big.
I said earlier that moving something doesn't change what it is, but that's not strictly true. If a planet shares its orbit with thousands of other planets, it's a member of a larger population. If it's the only thing in its orbit, it is essentially the population. This is the difference between being an object in that orbit and being the object in that orbit. The latter is a major planet – an IAU-sanctioned Planet™; I suppose you could also call them “individual planets”. (It's also the difference between being part of a loaf and being a sandwich. Plus or minus some filling, of course.)
Another of the IAU's criteria for Planets and Dwarf Planets is that they are generally round. Roundness is a useful criterion to describe planets, as it provides an overview of their size and structure and, crucially, the gravitational influence they exert over themselves and over nearby planets.
It's not an absolute, on/off, binary property though; there's no certain mass where you can add one more microgram of dust and the object suddenly stops being “not round” and instantly starts being “round”. It's a gradual thing, and it's subject to a lot of conditions, such as the body's composition and its temperature (which in turn is related to its distance from the Sun).
In fact, there are three general shapes corresponding to a planet's self-gravity: not round at all, round, and totally-über-super-well-round. I shall explain.
For a planet to qualify as an IAU Planet™ or Dwarf Planet™, it must be in hydrostatic equilibrium. This means that rather than being simply a cluster of rocks held together by their mutual gravitational attraction, a (Dwarf) Planet is massive enough that its own gravity distorts its shape into a sphere. The planet's rotation will also distort its shape into an ellipsoid, but that's inconsequential – it's the effect of the planet's gravity that's important.
Jupiter, Saturn, Uranus and Neptune are often referred to as Gas Giants; Uranus and Neptune are sometimes also referred to as Ice Giants. These names aren't particularly helpful – the composition of each planet can be classified and sub-classified as much as you like. So let's call them all “giant planets” for now. Like all (Dwarf) Planets, they are in hydrostatic equilibrium and like most things, they're made up of a variety of different substances.
But unlike other planets, a giant planet exerts so much gravitational force that there is no definite boundary between the layers of different substances inside the planet; the transitions between layers are smooth. There is no surface and no atmosphere, just a mostly-symmetrical sphere of stuff that gradually attenuates to nothing as you go further out. This is the aforementioned so-round-it-hurts state, and it's the same sort of thing as goes on inside a star. (This doesn't make giant planets stars, mind – there's no nuclear fusion happening inside giant planets.)
To avoid naming them by size, you might call these self-gravitationally-internally-smooth things “fluid planets”, as the entire the planet is in a fluid state. (“Gas planet” is a little misleading, because the pressure deep inside the planet can compress gases into liquids and solids.)
So, planets can be classified broadly into three categories: “spheroidal planets” in hydrostatic equilibrium, “fluid planets” with no definite layers or surface, and “irregular planets”, which includes anything else notable enough to be identified.
Everything is a planet. Even wee, small, diddy, tiny things are planets if you care enough about them to identify them.