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Jupiter's enormous gravity would turn its atmosphere first into a liquid from a certain depth, and then into a solid further towards its centre.
So Jupiter has a solid core, above which is a liquid layer and an atmosphere above that.
How is Jupiter fundamentally different than the (solid) inner planets? Why is Jupiter called a Gas Giant?
Jupiter being a gas giant is not about its appearance, as another answer stated. It's only about the mass distribution of a planet.
Jupiter's mass is 320 Earth masses, while we know from the Juno mission that the rock/ice in the core account for 5–25 of these Earth masses. So the rest of about 300 Earth masses is gas.
Thus Jupiter is a gas giant. It is really that simple. The more exotic states of matter that the solids in its interior probably exist in, don't affect the definition of a gas giant.
To put that into perspective:
Another way of inferring what Jupiter is made of, is taking a look at its average density. This is how it was done historically, before we had sophisticated computer models and high-pressure lab experiments.
Knowing Newton's laws, one can measure Jupiter's mass $M$ from its orbiting moons. Its size $r$ is known from the distance. Thus one can calculate its average density $\bar{\rho} = \frac{M}{4/3 \pi r^3}$ and finds a value of $\bar{\rho}_♃ = 1.326~\mathrm{g/cm^3}$. This is significantly lower than what Earth has ($\bar{\rho}_{\oplus} = 5.55~\mathrm{g/cm^3}$) and the other rocky planets.
Through simple weighted averaging with some rock mass of a few percent, it was then realized early on that one needs a lot of gas to reach such a low average density for such a planet as Jupiter.
An interesting detail here is, that one cannot build Jupiter of gas only, the resulting average density would be lower than the real one. This is how it was realized that some very dense material needs to exist somewhere in Jupiter, possibly a core of solid material.
One reason they are called gas giants is because they are mostly composed of elements that are gaseous at Earth like temperatures and pressures.
Jupiter is primarily composed of hydrogen with a quarter of its mass being helium, though helium comprises only about a tenth of the number of molecules.
Jupiter's upper atmosphere is about 88–92% hydrogen and 8–12% helium by percent volume of gas molecules. A helium atom has about four times as much mass as a hydrogen atom, so the composition changes when described as the proportion of mass contributed by different atoms. Thus, Jupiter's atmosphere is approximately 75% hydrogen and 24% helium by mass, with the remaining one percent of the mass consisting of other elements. The atmosphere contains trace amounts of methane, water vapor, ammonia, and silicon-based compounds. There are also traces of carbon, ethane, hydrogen sulfide, neon, oxygen, phosphine, and sulfur. The outermost layer of the atmosphere contains crystals of frozen ammonia. The interior contains denser materials - by mass it is roughly 71% hydrogen, 24% helium, and 5% other elements.[21][22] Through infrared and ultraviolet measurements, trace amounts of benzene and other hydrocarbons have also been found.
https://en.wikipedia.org/wiki/Jupiter
So Jupiter and Saturn are almost totally composed of hydrogen and helium, elements that are gaseous at Earth like temperatures and pressures. Of course the temperatures and pressures deeper inside Jupiter and Saturn are not exactly Earth like!
But the elements that they are composed of are commonly called gases even though they might be in exotic conditions such as liquid metallic hydrogen under the immense pressure and temperatures inside the planets. Most of us think of hydrogen and helium as gaseous elements, not liquids, or solids, or highly exotic forms of matter.
Thus Jupiter and Saturn are "gas giants".
A second reason they are called "gas giants" is historical. Famed science fiction writer James Blish wrote a science fiction story called "Solar Plexus", published in Astonishing stories, September, 1941. "Solar Plexus" was rewritten and republished in an anthology Beyond Human Ken, edited by Judith Merrill, 1954. The 1954 rewritten version contained the line:
A quick glance over the boards revealed that there was a magnetic field of some strength near by, one that didn't belong to the invisible gas giant revolving half a million miles away.
Science fiction readers who knew anything about the structure of giant planets thought that "gas giant" was a very fitting phrase to describe them. And some of them were professional astronomers. Thus the phrase began to be used by astronomers to describe the giant planets in the solar system.
Jupiter is composed primarily of gaseous and liquid matter. It is the largest of the gas giants, and like them, is divided between a gaseous outer atmosphere and an interior that is made up of denser materials. It's upper atmosphere is composed of about 88–92% hydrogen and 8–12% helium by percent volume of gas molecules, and approx. 75% hydrogen and 24% helium by mass, with the remaining one percent consisting of other elements.
The atmosphere contains trace amounts of methane, water vapor, ammonia, and silicon-based compounds as well as trace amounts of benzene and other hydrocarbons. There are also traces of carbon, ethane, hydrogen sulfide, neon, oxygen, phosphine, and sulfur. Crystals of frozen ammonia have also been observed in the outermost layer of the atmosphere.
The interior contains denser materials, such that the distribution is roughly 71% hydrogen, 24% helium and 5% other elements by mass. It is believed that Jupiter's core is a dense mix of elements – a surrounding layer of liquid metallic hydrogen with some helium, and an outer layer predominantly of molecular hydrogen. The core has also been described as rocky, but this remains unknown as well.
Do not assume that Jupiter has a solid core. Temperatures at the core have been estimated to be as high as 25000K. On the other hand, it's true that pressures are also very high. High pressures tend to lead to it being solid, while high temperatures tend to lead to it being a fluid. I don't think it is known which actually occurs. Under those conditions, it probably does not make sense to think of the material as being something that you would recognize as rock. They just know that there is a higher concentration of heavier elements.
I also think it's helpful to use the word "fluid" more than "liquid" in these cases. As you descend into Jupiter, the hydrogen gradually transitions from a gas to a supercritical fluid. It's not incorrect to call it a liquid, but, at those pressures, there's really no distinction between a gas and a liquid.
