Or is that simply a shorthand way of saying the plasma creating the magnetic field is moving which causes reconnection, etc.?
But the plasma is also described as moving because of the magnetic field moving!
So which is it? Anyone able to explain?
Here the building blocks are: 1.) moving charges and 2.) magnetic fields. As you correctly say moving charges produce magnetic fields(1). But magnetic field fields deflect charged particles via the Lorentz Force . This results in what is known as the frozen-in-condition that says that magnetic flux and the (highly conductive) plasma can only move together. 
Now, if the two things can only move together, which one gets to decide where to go? That depends on a parameter known as "plasma beta" . Basically it is the ratio between thermal pressure (of the particles) and magnetic pressure due to the field. In low beta plasma, the pressure of the magnetic field wins and the plasma is just along for the ride. This is the case in the solar corona and solar wind. In high beta plasma the plasma flows as it wishes (e.g. due to pressure gradients) and the magnetic field gets dragged along. This is the case e.g. inside the sun and the reason why the solar dynamo can work and produce magnetic fields.
(1) actually moving charges carry a current which causes a temporal change in electric field via Ampere's Law, the curl of which produces a magnetic field via Faraday's Law. 
No. Even in the absence of any charge at all, moving or otherwise, Maxwell's equations still have a nonzero solution. This is known as "light".
Magnetic fields from moving charges are pretty cool because you can show that they are equivalent to electric charges with relativistic effects due to charges' motions factored in. But thinking about relativistic motion equations for a huge number of particles is a tough starting point conceptually if you're just trying to find how a particle at a particular point in space will behave. So pragmatically, magnetic fields are a great conceptual tool. They also hold up straightforwardly once you bring in special relativity.
One thing that's very nice about electric/magnetic fields is that they are local. You can calculate the effect of magnetic forces on solar ejecta by just calculating the local field. It's much simpler conceptually to talk about how a particle will respond to a local magnetic field than it is to talk about how it will respond to a tremendous number of moving charges. It also ends up being very mathematically elegant; Maxwell's equations are very beautiful and conceptually simple, and their common applications are likewise beautiful and simple considering the seeming complexity of EM phenomena.
Furthermore, in some cases, like those involving light (EM waves propagating through space and time), you don't even have the luxury of knowing where the charges are that produced the field/how they moved: if a light wave is striking a piece of material from some distant light source, the only thing you know about/can measure is the field itself; it's therefore really nice to be able to do all of your calculations using the field.
But EM fields are more than just frameworks for understanding or calculating forces. They are very physical things. EM fields can literally carry linear/angular momentum and energy away from them. Let's say you have a satellite shaped like a long bar with two lasers at opposite ends pointing in opposite directions orthogonal to the main axis of the craft:
beam 1 points up -> |
| <- beam 2 points down
This comes up again in general relativity, where EM fields energy and momentum contribute to the curvature of spacetime in precisely the same way as mass does. In other words, if you had a huge amount of light passing through a region of space, it would be just as gravitationally attractive as an equivalent amount of mass (after converting units using E = mc^2).
When you think about it, conservation of momentum + the speed of light + EM fields' ability to move objects (i.e. change their mass and momenta) necessitates that they have this sort of physical reality. In the bar-satellite example, the laser beams are pushing back on the ship; since light doesn't travel infinitely fast, there is no equal-and-opposite reaction from some regular matter that the EM fields would mediate instantaneously, i.e. no regular matter that's pushing against the satellite to get it spinning (as would be the case with a regular thruster used for stationkeeping). The momentum has to go somewhere; as it turns out, it goes into the field itself in an extremely well-defined way.
So, again, EM fields are the real deal; moving charges contribute to fields, but the fields themselves have their own well-measured, well-described physical reality in classical physics.
Magnetism creates a rotation of the path of the moving particles. It can also create magnetic breaking, like eddy currents. The rotation is always reducing the present magnetic field. That is because of EM and conservation of energy.
You can see that in the video of the article. The current follows circle around the magnetic field. And it is fed from the charged centre.
In the case that the magnetic field is reducing in strength, we get a different reaction. A decreasing magnetic field creates currents that sustain the field. This principle can also cause electromagnetic waves.
The NASA theory is that the plasma somehow sustains the magnetic field. And that this magnetic field is localized to long flux-lines.
Their theory is based on the observation of plasma ropes on the sun. With detectors one can find strong Zeeman effects at the start and end of these plasma ropes. And recently they found even stronger effects at the rope itself. The zeeman effect is related to the magnetic field. So their conclusion is that the rope somehow follows a magnetic field-line. This means that the electrons and ions must spiral through these solar ropes. They also assume for simplicity that no electric fields can exist.
When 2 solar-ropes connect, we sometimes get solar flares. So this creates the idea of magnetic reconnection. Some astronomers even go so far to claim that the flux-lines actually exist. And that these flux-lines create energy with a collision.
But because it is counter our laboratory observations, it seems to me that the problem is a lot simpler. The solar-rope are currents that create magnetic fields instead.
But we can go a small step further. The zeeman effect is also very similar to the Stark effect. And this might indicate that we have strong electric fields at the surface of the sun. And this means we have also found the driving force of the currents inside the solar ropes.
And if 2 solar ropes connect, we will likely have an electrical shortcut. Which is as we all know,
But let's use the models on this big solar-rope (Loop) on the sun.
We can see movement of plasma very well in this video.
The bright plasma follows some curved lines downward and sometimes upwards.
You can also see other solar ropes behaving similar.
The plasma is probably fed by dark mode plasma (cloudy area).
We see no spiralling. And I have no idea how we can explain this phenomenon with NASA's model.
If I use the corrected model, the plasma simply follows the electric currents.
And the plasma follows gravity when it is neutral or almost neutral.
That can happen when the particles combine as molecules.
The currents create magnetic fields themselves that can cause the curve that we see.
So we can expect quite some magnetic field here.
The magnetic field even helps the curve to rise up from the surface.
But having other ideas is not the way to get into astronomy.