I think there are a few things going on here, but I'll try to at least help clarify the situation (and give you some response.)
The section in your link about datums and ellipsoids is simply emphasizing that there is no such thing as one correct description of a location (i.e. coordinates.) All coordinate values are measurements based on some set of standards - the shape of the surface of our planet, the dimensions of the axes, etc. And on top of that, nothing on our planet is truly fixed in place - the continents move as well as change shape over time. Some of this did not really matter many years ago when a) it was not possible to make precise measurements (by today's standards) over long distances and b) the interest in positions was mostly about navigation, so precise location (even to tens of meters) was often less important. As both our capabilities and interest in making long precise measurements have increased, we've become more aware of these issues and worked to quantify them. However, depending on the situation and needs, different solutions work better. I hope it's obvious that it is easier to come up with a set of parameters that closely matches reality for a limited area - say, one country or even one continent - than for the entire world. So the really important point here is that you must be aware of what datum you are working in, which (now) includes the time frame of the measurements. And you should document this for any measurements you make (metadata) as well as find out what the datum is for any measurements you are working with (acquired from others.)
Another important element to remember is that all of these are measurements, which are inherently imperfect and involve some inaccuracy. Sure, hypothetically there may be "true" values for a position, but they will never be definitively known. So the best we can do is measure as well as we can and document what we did and how, so that a reliable comparison (another measurement) can be made with our information later.
Also, if you're getting into the raw measurements of different receivers, (outputting raw values from a receiver to another system for processing,) you should be aware of the phase center of your antenna. Each antenna design has its own characteristics that define where the "center" of it functionally is - the point where the measurements to satellites are referenced. Manufacturers generally give you a measuring point so that you can determine the height above the ground (or whatever you are measuring to) and software handles any offset from there. Depending on the design, it may also be important to orient your receiver - such as facing it north - so that any horizontal offset or eccentricity can be accurately accounted for. I don't know how readily available all manufacturers make this information, but one good source is the U.S. National Geodetic Survey at https://www.ngs.noaa.gov/ANTCAL/index.xhtml. (The NGS site also has lots of good information on global postioning - but realize that they are working on a high-complexity level and broad scale, so some of the information may be difficult to make use of.)
So, to your question - yes, you should be able to use a position calculated from one receiver as the input location for another. Assuming you are working within one consistent datum/coordinate system. (For example, you could set up a static observation with one receiver to determine coordinates for a point, and then later set up a different receiver as a RTK base station over that point and enter your coordinates for that location.) But remember that all of these measurements have errors and the errors compound - if your first position was within +/- 1 cm (95% confidence) and then you measure to another location (referenced to that first position) within +/- 1 cm (95% confidence), then your second location is, at best, +/- 2 cm.
Again, I hope this is some help to you. Best of luck to you!