Sound is only a wave form transmitted by the oscillation of atoms. They can be any atoms. It’s not a fundamental force.
Electromagnetism is a fundamental force transmitted by its very own special particle called a photon. However, the true nature of the photon is that it exhibits both wavelike and particle-like properties (called wave-particle duality).
So the answer is that photons move through space. They actually do go from point A to point B. They also are a wave at the same time. Photons that move one at a time still can exhibit wave like behavior (e.g., creating wavelike interference patterns despite having only been sent one at a time).
How a point particle can also be a wave seems contradictory. Really, it’s just our inability to conceptualize such a thing. Just like a fully colorblind person can’t imagine the color red, we have difficult imagining how a photon can be both point particle and wave.
Electromagnetic waves are, as the name may imply, not sound waves. Waves do not actually require a medium to exist in. Only mechanical waves, a specific subset of waves including sound and gravity waves (not *gravitational* waves, but waves caused by gravity like water waves) requires a medium to travel through.
Light waves exist independent of a medium – they are fluctuations in the local electric and magnetic fields, which perpetuate themselves outwards indefinitely.
A photon is a oscillation in the electric and magnetic field. These oscillations are at right angles to each other and not in phase with each other. The changing electric and magnetic fields then generate each other with no medium required anymore than your car needs a medium to move forward. Once the photon is emitted, it oscillates like a tiny pendulum as it moves along until it finds another charged particle to transfer its momentum to.
Sound is a mechanical wave, literally the vibration of atoms.
Electromagnetic waves are force carries of the electromagnetic force. As in, all through spacetime there is an electromagnetic field, this field produces energy excitations, this is what a photon is.
It is not actually a wave, we only describe it as this when we use the Schrodinger (and other) interpretation(s) of quantum mechanics.
Everyone else has made good answers, so I won’t go into the full explanation, but you should know that sound waves travel in TWO ways – one is compressional like you described. It’s like you take a slinky, secure it at one end, stretch it, and give it a quick push — you’ll see the compression wave travel down the slinky.
The other is a longitudinal wave. It’s as if you took the same slinky and moved it from side to side on the table, and you’d see waves with peaks and valleys appear. Both aspects are critical for sound transmission.
You have asked a very good question.
When the physicists a century ago started studying light as an electromagnetic wave, they expected to find some sort of medium for the waves to travel through.
The fact that there was no such medium, and that the speed at which they propagate (a.k.a. the spped of light) is constant regardless of the speed of the observer led to the Theory of Relativity.
The idea that electromagnetic waves need something to travel through was only disproved around the turn of the 20th century. The medium that was conjectured for light as air is for sound was called [luminiferous aether](https://en.wikipedia.org/wiki/Luminiferous_aether), and its name is memorialised in ethernet where (in the original design) the single co-axial cable linking all the machines fulfilled the same role.
The existence of luminiferous aether was strongly argued against by the [Michelson-Morley Experiment](https://en.wikipedia.org/wiki/Michelson–Morley_experiment) in the late 1880s, which showed that the speed of light is constant in every direction and therefore cannot be influenced by the earth’s passage through a stationary aether. It’s not a proof: you can conjecture something aetherous-like which would still “work” with the Michelson-Morley experiment (perhaps the aether is dragged along by the earth?) but such things look like special pleading. [Special relativity](https://en.wikipedia.org/wiki/Special_relativity), published 1905, and its various confirmatory experiments killed aether off completely.
First of all, this is an excellent question – which has *really* bugged people in the 19th century to no end. To solve it, they even propose that there is an universal medium, “aether” permeating everything in which those waves, well do the waving. A clever experiment was devised by Michelson and Morley to exploit the fact that the Earth would have to move relative to the aether while orbiting the Sun and this would reflect in the speed of light being different in different directions. The experiment famously failed to find the effect. Some time later, the Special Theory of Relativity was built basically on these findings, explaining why the hell is it possible that the speed of light is the same not only in all directions, but for all observers, no matter how much they move themselves. But that’s a long and complicated story.
As for “what makes the wave”, there is no one answer, especially now that we know about quantum field theory and photons and stuff. But the most straightforward explanation lies in the Maxwell equations, which is a set of 4 formulas that tell you, when magnetic ans electric fields happen. Not going into dirty details, the important part is that in these equations, any change of electric field with time causes the appearance of magnetic field and vice versa. So now imagine the wave that starts maybe as a change in the electric field in your antena in your cellphone. This change creates magnetic field – but this appearing magnetic field is a change with respect to no magnetic field before, so it creates electric field – in an endless pattern! This sounds like a cartoon, but it’s actually exactly how the wave solutions of the Maxwell equations looks like, as in those, both fields change periodically, with the maximum of one corresponding to the minimum of the other.
Electricity makes magnetisim. Magnetisim makes electricity. Light is those two dancing back and forth hundreds trillions of times a second. When they dance slower, they have less energy and are infrared or radio. When they dance faster, they have more energy and are ultraviolet or x rays.
You can prove there’s no “thing” they’re vibrating because the speed of light is exactly the same in all directions no matter how fast you’re moving.
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