I add my comment as a follow up to the question in chemistry SE.
The problem is due the fact that typical explanation of electrons and orbitals depict them as "boxes" or "orbits" in which electrons reside. This is due to historical reasons, but it compromises the understanding of this topic.
Electrons don't "reside" in orbitals. Orbitals describe electrons in space. Saying that they reside in orbitals would be like saying that you reside in a box labeled "human". The reality is that you are a human.
An orbital is nothing but one of many convenient 3d (let's not involve spin for simplicity) functions that has nice properties. They all belong to a Hilbert space, which is simply a bunch of functions. These functions share interesting properties, such as that they are orthogonal when centered on the same point in space, that they are not null, and that they solve one specific problem exactly: the problem of a single positive charge interacting with a single negative charge.
That's it. They are nothing more than the x and the y axis on a plane. You choose them orthogonal because it's practical, and you use them to decompose whatever vector you might handle in a x component and a y component. But the vector you handle is not "residing" on the x axis or the y axis. If you had a vector lying down on the x axis (or close to), you would say "it is pointing in the positive x direction" or "it's well described by the x axis" because it has a strong x component and barely no y component, exactly as you would say a given electronic distribution is well described by an
s orbital because it has mostly
s orbital component. This is what is meant when chemists say "it's in an s orbital", but it's deceiving and for all purposes incorrect.
Are there actual "dwelling orbitals" which are the result of linear combination of these calculated orbitals?
There are charge (and probability) distributions of a single electron, yes. You can compute it if you want, and it might make sense or not make sense, depending on the context, and this charge distribution may or may fit a physical shape that you expect or not, depending on the molecule shape, external factors (fields, light),
In other words, for a given set of calculated orbitals and coefficients, does the resulting well-define shape represent an actual "charge density blob" in which 2 electrons (out of all the electrons in the system) reside?
Only the total sum (the total density). If you want the one-electron density, you might have some degrees of freedom in how you extract it, meaning that there are multiple ways (within limits) of decomposing that total density into one-electron densities, and they are equivalent, exactly as 5 can be decomposed in 4+1 or 2+3.
Edit: in the article you added, you are seeing an image obtained from tunneling effect. What happens there is that you basically "tune" the tip of the AFM to "resonate" so that electrons can jump from/to the "orbital" with the same energy.
Note the massive use of quotes. What happens there is that you are probing electron density at a given energy level and in every specific point in space. Electron density is what you measure, and yes, electron density is, on strictly speaking inaccurate but correct practical terms, determined by the orbital. However, once again, it's not so simple. The reality is that you can use the orbital (what you obtain from solving the eigenvalue problem) to express that electron density, and that expression is pretty much spot on. However, depending on the methodology you use, you can transform the orbitals into an equivalent set that has a specific property. For example, you might combine them to provide an absolutely equivalent set that is instead localized, meaning that you won't get orbitals similar to that shape. You will instead get orbitals that describe a C-C bond, for example, or a C-H bond.
So, your point is somehow valid. There are physical electronic spatial distributions for a given energy that resemble the orbitals that you obtain from a computation, but what you are probing is a physical entity at a specific energy. Orbitals are a mathematical construct that, within some constraints, match the physical data you obtain from the AFM imaging, but it is due to the nature of the experiment, and the nature of the method.
The difference seems to be academic and pretty much pointless. It is indeed a subtle difference, but it's far from pointless.