“You know what always fucks me up? The solar wind. Like, the sun is...”
Please elaborate on us technically living inside a star. I love this stuff.
OKAY, so! If you look up at the sun in the sky you see a well-defined circle, right? And you can watch (eg. in images like this) the sun rotating, and it looks kind of like a solid ball, right? Sort of. Maybe. WELL! That’s not really the case at all. At that “boundary”, the density of material drops off very quickly, so it goes from about the density of air inside it to much, much less dense outside. So in that sense it is a boundary. This is called the photosphere. Outside it is the corona. (Here’s a diagram that shows these layers!)
Interesting fact! the reason you can “see” the material in the photosphere in the visible range of the spectrum, basically, is that the higher density means the particles are close enough together that light has a large probability of hitting and interacting with particles there. It’s called being “optically dense”, and it’s basically an effect of the light our eyes can see interacting with a denser material. (In different wavelengths, you can see to different levels! My fave is extreme ultraviolet/X-rays, because you can see a lot of cool stuff going on in the corona with that! but anyway...)
If we head outwards (into the corona) the density decreases, as I mentioned. Lower density means that the particles are really far apart, to the point that statistically, it’s very likely that any light will just go right through and never hit any of particles. Emission of light (why we see the sun glowing) happens when light interacts with particles, which is why we see a LOT less emission in the corona than in the photosphere. So the corona is a lot dimmer, making the photosphere look like a solid boundary or “shell” in comparison. Which is what we see as the round ball in the sky we all know and love.
Why is this relevant? Well, the point is, you can’t “see” the corona in the same way (well you can at solar eclipse, when your eyes/cameras are not overwhelmed by all the light coming from the photosphere) but it does have material in it, and even if it's a lot less dense than the photosphere and the stuff below it. (Side note: it's got one thing: the corona is HOT. Like, a hundred times the temperature of the level just below it. We don't actually really understand why this is the case, and it's one of the biggest mostly-open questions in solar physics that people argue about.)
ANYWAY. So the other thing about the corona is that it’s basically all flowing outwards, propelled by the explosive power stored by the "twisting up" of magnetic fields. These have a thing called magnetic tension, in that they "don't like" to be twisted; it costs energy to do so (think of a rubber band getting twisted tighter and tighter and how it springs back with a lot of force at some point! That's basically what magnetic fields are like!) But it gets twisted up as the sun rotates, and at some point (usually about once every eleven years, as it happens), the sun's magnetic field gets too "twisty" and knotted/tangled up by the spinning, and it has to spring back. This part of the “solar cycle” releases a lot of energy, and magnetic field, and plasma, into the solar system.
.....Okay that was a slightly simplified picture of the solar cycle. In reality, this isn't a one off event. It's actually happening all the time, lots of little explosions of material to release tension (though they’re more frequent and violent at the maximum of the solar cycle) and together they fling plasma out into the solar system. (Think of it like a big cloud of debris!) It basically flows out in all directions, but there really isn't a definitive point at which is stops being the corona/atmosphere and starts being the solar wind.
You could argue that the photosphere is the "surface" of the sun, but even this is tenuous; if you could somehow "stand" at what we see as the surface without burning up, you wouldn't be able to stand at all; you'd just fall in because there's nothing “solid” there. (It’s a comparable density to air on earth, just... a lot hotter)
The reason it does stop in the end is that the further the corona goes, the larger is the sphere that it is “spread out” over, so it becomes so, so thin that it’s hardly there at all. Again, there isn’t really a set “boundary” for where this happens. But magnetic fields, as usual, tend to rule all in the solar system, so the “heliopause”, or edge of the “heliosphere” is basically the line where the sun’s magnetic field has decreased in strength to the extent that the interstellar (background) magnetic field is stronger than it. Since the material that makes up the solar wind is basically “joined” to the magnetic field, that’s kind of the point at which you can say the sun’s atmosphere “ends”. However, this is well outside the distance at which the planets orbit, so yeah we all... sort of orbit around within it, shielded by our planet’s own magnetic field.
(Another interesting fact! The heliopause is about, in fact, where the Voyager spacecraft have reached now! I don’t know if you heard but a few years ago there was news that they’d come close to the edge of the heliosphere. But no one’s very sure, as it’s hard to get data from them when they’re that far out, and also as I said it’s a bit of a fuzzy boundary anyway.)
So! TL:DR.... we see the sun as having a boundary because it has a sharp change in density at that point, which affects emission of light. However, it is essentially a big blob of gas which is constantly being pushed out into the solar system, and that doesn't really "end" until much, much further out, beyond all the planets and certainly beyond earth's orbit. That's the sense in which we live within a star's atmosphere!