Yes. This is precisely what is being said. It is both at once, such is the paradox of QM. I've been partial to saying it is both a wave and a particle.
The idea of waves and particles have a history. By that I mean the words themselves and the way they came to be used in physics have a history. Particles and bodies described
things, and the were incorporated into physics rather naturally, as even before Newton the sense of "body" as in "celestial body" or other physics uses was present:
" Loke þou haue a strong vessel..& loke þat þe couercle þerof & þe bodi be wel closyng"
"Man hath of eorþe al is bodi..of watere..wete, Of þe Eyr..breth..of fuyr..hete"
Interestingly, one of the earliest "physics"-type usage of particle and body comes from the same line: "An element is symple and lest particle of a body þat is compowned"
Over time, as physics matured and more nuanced, technical definitions were required, such definitions were formulated. And when later physicists came to understand that physics wasn't just mechanics ("bodies" at rest or not at rest and force), but that fields, light, energy, and various other terms needed to be included they were.
The important point is that even as definitions changed, they did so in particular ways. Particles were something very specific, in that by the 19th and early 20th century if something didn't have particular properties it wasn't a particle. The same is true for waves. Most importantly, they are defined in opposition to one another, and deliberately so.
The reason oscillations that result in the interpretation of sounds are called waves is older than physics, and naturally came from ocean waves. However, before physics had "waves" like sound waves, there was already a sense of "wave" that had nothing to do with water but did have to do with vibrations of matter: "The holy organ rolling waves Of sound on roof and floor"
"o what is that sound that so trills the ear"
Like particles, this sense was made technical. It meant something quite specific, because waves in physics did things that particles could not. An entirely different formulation was required to describe each, because particles were
things, and occupied a specific space at specific times and moving (even if the movement was 0) along specific trajectories.
Waves were not localized. By the time waves was defined in physics the waves of the ocean weren't technically waves anymore. Rather, the waves were the oscillations or vibrations that propagated through water, but they were not made of water.
It is not a simple thing to simply say that e.g., electrons are both waves and particles. This is like saying that a cat is both alive and dead. It is a description of one thing as being in two mutually exclusive states. A particle
cannot ever be a wave, and vice versa.
This is something I've been wondering about which QM does not supply an answer for. All I can say is what I think is occurring, as you mentioned it seems as though the particle is interfering with itself which I agree with.
The interference effect describes the ways in which two or more waves alter when they collide/meet/hit one another. Even in the technical sense, interference is supposed to require some specific thing that some other thing or things interfere with.
To say a thing interferes with itself, which seems to be the case here, means that it isn't a thing at all. The only way it can interfere with itself is if it is both itself and something else at the same time.
What I infer from the experiment is that the particle is going through one slit while its superposition goes through the other slit, this superposition, being in two places at once, explains away the wave like interference pattern being produced.
Superposition is a single state of a single system. It's defined that way. However, what that means is that this single state of the system has more than one set of coordinates or is a system characterized by more than one mutually exclusive set of properties (like position).
Where I run into an issue is when people start saying things like the particle "knew" which slit to go through or which box to choose however all I see is a different experimental setup further interfering with the already interfering particles.
That's the delayed-choice experiment. The idea behind it is as follows:
We know that we get the interference pattern, even with one electron going through the double-slit screen at a time. We also know that if we set up any kind of device to try to detect which slit the electron goes through (either by having some kind of device at the slit, or by using some telescope or imagine equipment to "see" which slit the electron travels through), the interference pattern disappears.
The reason we have descriptions like "knew" or "knows" is due to J. A. Wheeler's delayed-choice experiment. The set-up is the same as the double-slit experiment, with the electron gun, the double-slit screen and the detection screen. The only difference is that we have detection equipment (like a telescope) set-up
behind the detection screen. So we start the experiment and the electrons start hitting the detection screen one at a time, and the interference pattern starts to show up. Moreover, this is a continuous stream, so even though only one electron travels through the double-slit screen at one time, there's always one close behind and close in front.
In the middle of the experiment, with the interference pattern already forming, and electrons which would (if we kept the detection screen in place) still hit in spots that continued to make-up the interference pattern, we remove the detection screen. Now (presumably), the electrons which were about to hit it can be detected by the telescope device set-up already behind the screen we've just removed. So now we should be able to see which slit electrons are travelling through and how they are forming this interference pattern.
Only we don't. Not only do we not see this, but the interference pattern stops. Which means that the photons which had already gone through the double-slit screen, and which would (had we not removed it) hit the detection screen in a place that we'd expect (knowing that it is already "interfered" with), have somehow "known" that they would be observed. And they hit the screen the way a particle would.
In the simplest terms, we have electrons travelling at the screen about to hit in the places we'd expect given interference. If we left the screen in place, they'd hit these places. However, when we remove the screen to "detect" the trajectory of the particles, they will not even be travelling along a trajectory that would form the interference pattern.